Subir Sachdev

Last updated

Subir Sachdev
R36C4122s.jpg
Born2 December 1961
New Delhi
Alma mater
Known for Sachdev–Ye–Kitaev model
Awards
Scientific career
Fields Condensed matter theory
Thesis Frustration and Order in Rapidly Cooled Metals  (1985)
Doctoral advisor D. R. Nelson
Website sachdev.physics.harvard.edu

Subir Sachdev is Herchel Smith Professor of Physics [1] at Harvard University specializing in condensed matter. He was elected to the U.S. National Academy of Sciences in 2014, received the Lars Onsager Prize from the American Physical Society and the Dirac Medal from the ICTP in 2018, and was elected Foreign Member of the Royal Society ForMemRS in 2023. He was a co-editor of the Annual Review of Condensed Matter Physics 2017–2019, [2] [3] and is Editor-in-Chief of Reports on Progress in Physics 2022-.

Contents

Sachdev's research describes the consequences of quantum entanglement on the macroscopic properties of natural systems. He has made extensive contributions to the description of the diverse varieties of entangled states of quantum matter, and of their behavior near quantum phase transitions. Many of these contributions have been linked to experiments, especially to the rich phase diagrams of the high temperature superconductors. Sachdev's research has exposed remarkable connections between the nature of quantum entanglement in certain laboratory materials, and the quantum entanglement in astrophysical black holes, and these connections have led to new insights on the entropy and radiation of black holes proposed by Stephen Hawking.


Honors

Subir Sachdev has made profound contributions to theoretical condensed matter physics research. His main interests have been in quantum magnetism, quantum criticality, and perhaps most innovative of all, links between the nature of quantum entanglement in black holes and strongly interacting electrons in materials.

Professor Subir Sachdev is a world renowned condensed matter theorist, with many seminal contributions to the theory of strongly interacting condensed matter systems. He is a pioneer in the study of systems near quantum phase transitions. He has also pioneered the exploration of the connection between physical properties of modern quantum materials and the nature of quantum entanglement in their many-particle state, elucidating the diverse varieties of entangled states of quantum matter.

Subir Sachdev has made pioneering contributions to many areas of theoretical condensed matter physics. Of particular importance were the development of the theory of quantum critical phenomena in insulators, superconductors and metals; the theory of spin-liquid states of quantum antiferromagnets and the theory of fractionalized phases of matter; the study of novel deconfinement phase transitions; the theory of quantum matter without quasiparticles; and the application of many of these ideas to a priori unrelated problems in black hole physics, including a concrete model of non-Fermi liquids.

for his seminal contributions to the theory of quantum phase transitions, quantum magnetism, and fractionalized spin liquids, and for his leadership in the physics community.

The Dirac Medal was awarded to Professor Sachdev in recognition of his many seminal contributions to the theory of strongly interacting condensed matter systems: quantum phase transitions, including the idea of critical deconfinement and the breakdown of the conventional symmetry based Landau–Ginsburg–Wilson paradigm; the prediction of exotic 'spin-liquid' and fractionalized states; and applications to the theory of high-temperature superconductivity in the cuprate materials.

Sachdev has made seminal advances in the theory of condensed matter systems near a quantum phase transition, which have elucidated the rich variety of static and dynamic behavior in such systems, both at finite temperatures and at T=0. His book, Quantum Phase Transitions, [11] is the basic text of the field.

Career

Sachdev attended school at St. Joseph's Boys' High School, Bangalore and Kendriya Vidyalaya, ASC, Bangalore. He attended college at Indian Institute of Technology, Delhi for a year. He transferred to Massachusetts Institute of Technology where he received a B.S. in Physics. He received his Ph.D. in theoretical physics from Harvard University. He held professional positions at Bell Labs (1985–1987) and at Yale University (1987–2005), where he was a Professor of Physics, before returning to Harvard, where he is now the Herchel Smith Professor of Physics. He has also held visiting positions as the Cenovus Energy James Clerk Maxwell Chair in Theoretical Physics [19] at the Perimeter Institute for Theoretical Physics, and the Dr. Homi J. Bhabha Chair Professorship [20] at the Tata Institute of Fundamental Research.[ citation needed ] He has also been on the Physical Sciences jury for the Infosys Prize from 2018. [21]

Books

Research

See selected papers with commentaries.

Sachdev has studied the nature of quantum entanglement in two-dimensional antiferromagnets, introducing several key ideas in a series of papers in 1989-1992. He has developed the theory of quantum criticality, elucidating its implications for experimental observations on materials at non-zero temperature. In this context, he proposed [22] a solvable model of complex quantum entanglement in a metal which does not have any particle-like excitations: an extension of this is now called the Sachdev-Ye-Kitaev (SYK) model. These works have led to a theory of quantum phase transitions in metals in the presence of impurity-induced disorder, and a universal theory of strange metals [23] which applies to a wide variety of correlated electron materials, including the copper-oxide materials exhibiting high temperature superconductivity. Many puzzling features of the `psuedogap' phase of these materials are also resolved by these theories. A connection between the structure of quantum entanglement in the SYK model and in black holes was first proposed by Sachdev, [24] and these connections have led to extensive developments in the quantum theory of black holes.

Quantum criticality, superconductors, and black holes

Extreme examples of complex quantum entanglement arise in metallic states of matter without quasiparticle excitations, often called strange metals. Such metals are invariably present in higher temperature superconductors, above the highest transition temperatures for superconductivity. The strange metallicity and superconductivity are manifestations of an underlying quantum critical state of matter without quasiparticle excitations. Remarkably, there is an intimate connection between the quantum physics of strange metals in modern materials (which can be studied in tabletop experiments), and quantum entanglement near black holes of astrophysics.

This connection is most clearly seen by thinking more carefully about the defining characteristic of a strange metal: the absence of quasiparticles. In practice, given a state of quantum matter, it is difficult to completely rule out the existence of quasiparticles: while one can confirm that certain perturbations do not create single quasiparticle excitations, it is almost impossible to rule out a non-local operator which could create an exotic quasiparticle in which the underlying electrons are non-locally entangled. Using theories of quantum phase transitions, Sachdev argued [11] [25] instead that it is better to examine how rapidly the system loses quantum phase coherence, or reaches local thermal equilibrium in response to general external perturbations. If quasiparticles existed, dephasing would take a long time during which the excited quasiparticles collide with each other. In contrast, states without quasiparticles reach local thermal equilibrium in the fastest possible time, bounded below by a value of order (Planck constant)/((Boltzmann constant) x (absolute temperature)). [11] Sachdev proposed [22] [26] a solvable model of a strange metal (a variant of which is now called the Sachdev–Ye–Kitaev (SYK) model), [27] which was shown to saturate such a bound on the time to reach quantum chaos. [28]

We can now make the connection to the quantum theory of black holes: quite generally, black holes also thermalize and reach quantum chaos in a time of order (Planck constant)/((Boltzmann constant) x (absolute temperature)), [29] [30] where the absolute temperature is the black hole's Hawking temperature. And this similarity to quantum matter without quasiparticles is not a co-incidence: Sachdev argued [24] that the SYK model maps holographically to the low energy physics of charged black holes in 4 spacetime dimension. Also key to this connection was the fact that charged black holes have a non-zero entropy in the limit of zero temperature, as does the SYK model when the zero temperature limit is taken after the large size limit. [31]

These and other related works on quantum criticality by Sachdev and collaborators have led to valuable insights on the properties of electronic quantum matter, and on the nature of Hawking radiation from black holes. Solvable models related to gravitational duals and the SYK model have led to the discovery of more realistic models of quantum phase transitions in the high temperature superconductors and other compounds. Advances in the theory of quantum transitions in metals in the presence of impurities have led to a universal theory of strange metals which applies across a wide range of correlated electron compounds. Such predictions [32] [33] have been connected to experiments on graphene [34] [35] and the cuprate superconductors. [36] The SYK model plays a key role in the computation of the density of low energy quantum states of non-supersymmetric charged black holes in 4 spacetime dimensions, [37] [38] and provides the underlying Hamiltonian system upon which advances on the Page curve of entanglement entropy of evaporating black holes have been based. [39]

Sachdev has also developed the theory of critical quantum spin liquids which feature fractionalization and emergent gauge fields, along with absence of quasiparticles. Such spin liquids play an important role in the theory of the cuprate superconductors.

Resonating valence bonds and Z2 quantum spin liquids

P.W. Anderson proposed [40] that Mott insulators realize antiferromagnets which could form resonating valence bond (RVB) or quantum spin liquid states with an energy gap to spin excitations without breaking time-reversal symmetry. It was conjectured that such RVB states have excitations with fractional quantum numbers, such as a fractional spin 1/2. The existence of such RVB ground states, and of the deconfinement of fractionalized excitations was first established by Read and Sachdev [41] and Wen [42] by the connection to a Z2 gauge theory. Sachdev was also the first to show that the RVB state is an odd Z2 gauge theory, [43] [44] [45] . An odd Z2 spin liquid has a background Z2 electric charge on each lattice site (equivalently, translations in the x and y directions anti-commute with each other in the super-selection sector of states associated with a Z2 gauge flux (also known as the m sector)). Sachdev showed that antiferromagnets with half-integer spin form odd Z2 spin liquids, and those with integer spin form even Z2 spin liquids. Using this theory, various universal properties of the RVB state were understood, including constraints on the symmetry transformations of the anyon excitations. Sachdev also obtained many results on the confinement transitions of the RVB state, including restrictions on proximate quantum phases and the nature of quantum phase transitions to them.

The topological order (i.e. ground state degeneracies on 2-manifolds) and anyons of Z2 quantum spin liquids are identical to those which appeared later in the solvable toric code model, which plays a key role in quantum error correction in qubit devices.

Z2 spin liquids are ground states of spin models on the kagome lattice, and this has been connected to experiments on correlated electron materials and arrays of trapped Rydberg atoms.

Related Research Articles

<span class="mw-page-title-main">Condensed matter physics</span> Branch of physics

Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases that arise from electromagnetic forces between atoms and electrons. More generally, the subject deals with condensed phases of matter: systems of many constituents with strong interactions among them. More exotic condensed phases include the superconducting phase exhibited by certain materials at extremely low cryogenic temperatures, the ferromagnetic and antiferromagnetic phases of spins on crystal lattices of atoms, the Bose–Einstein condensates found in ultracold atomic systems, and liquid crystals. Condensed matter physicists seek to understand the behavior of these phases by experiments to measure various material properties, and by applying the physical laws of quantum mechanics, electromagnetism, statistical mechanics, and other physics theories to develop mathematical models and predict the properties of extremely large groups of atoms.

<span class="mw-page-title-main">Superconductivity</span> Electrical conductivity with exactly zero resistance

Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike an ordinary metallic conductor, whose resistance decreases gradually as its temperature is lowered, even down to near absolute zero, a superconductor has a characteristic critical temperature below which the resistance drops abruptly to zero. An electric current through a loop of superconducting wire can persist indefinitely with no power source.

<span class="mw-page-title-main">Fermi liquid theory</span> Theoretical model in physics

Fermi liquid theory is a theoretical model of interacting fermions that describes the normal state of the conduction electrons in most metals at sufficiently low temperatures. The theory describes the behavior of many-body systems of particles in which the interactions between particles may be strong. The phenomenological theory of Fermi liquids was introduced by the Soviet physicist Lev Davidovich Landau in 1956, and later developed by Alexei Abrikosov and Isaak Khalatnikov using diagrammatic perturbation theory. The theory explains why some of the properties of an interacting fermion system are very similar to those of the ideal Fermi gas, and why other properties differ.

In condensed matter physics, a quasiparticle is a concept used to describe a collective behavior of a group of particles that can be treated as if they were a single particle. Formally, quasiparticles and collective excitations are closely related phenomena that arise when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in vacuum.

The fractional quantum Hall effect (FQHE) is a physical phenomenon in which the Hall conductance of 2-dimensional (2D) electrons shows precisely quantized plateaus at fractional values of , where e is the electron charge and h is the Planck constant. It is a property of a collective state in which electrons bind magnetic flux lines to make new quasiparticles, and excitations have a fractional elementary charge and possibly also fractional statistics. The 1998 Nobel Prize in Physics was awarded to Robert Laughlin, Horst Störmer, and Daniel Tsui "for their discovery of a new form of quantum fluid with fractionally charged excitations" The microscopic origin of the FQHE is a major research topic in condensed matter physics.

<span class="mw-page-title-main">Topological order</span> Type of order at absolute zero

In physics, topological order is a kind of order in the zero-temperature phase of matter. Macroscopically, topological order is defined and described by robust ground state degeneracy and quantized non-Abelian geometric phases of degenerate ground states. Microscopically, topological orders correspond to patterns of long-range quantum entanglement. States with different topological orders cannot change into each other without a phase transition.

<span class="mw-page-title-main">Majorana fermion</span> Fermion that is its own antiparticle

A Majorana fermion, also referred to as a Majorana particle, is a fermion that is its own antiparticle. They were hypothesised by Ettore Majorana in 1937. The term is sometimes used in opposition to a Dirac fermion, which describes fermions that are not their own antiparticles.

A quantum critical point is a point in the phase diagram of a material where a continuous phase transition takes place at absolute zero. A quantum critical point is typically achieved by a continuous suppression of a nonzero temperature phase transition to zero temperature by the application of a pressure, field, or through doping. Conventional phase transitions occur at nonzero temperature when the growth of random thermal fluctuations leads to a change in the physical state of a system. Condensed matter physics research over the past few decades has revealed a new class of phase transitions called quantum phase transitions which take place at absolute zero. In the absence of the thermal fluctuations which trigger conventional phase transitions, quantum phase transitions are driven by the zero point quantum fluctuations associated with Heisenberg's uncertainty principle.

<span class="mw-page-title-main">String-net liquid</span> Condensed matter physics model involving only closed loops

In condensed matter physics, a string-net is an extended object whose collective behavior has been proposed as a physical mechanism for topological order by Michael A. Levin and Xiao-Gang Wen. A particular string-net model may involve only closed loops; or networks of oriented, labeled strings obeying branching rules given by some gauge group; or still more general networks.

Quantum dimer models were introduced to model the physics of resonating valence bond (RVB) states in lattice spin systems. The only degrees of freedom retained from the motivating spin systems are the valence bonds, represented as dimers which live on the lattice bonds. In typical dimer models, the dimers do not overlap.

<span class="mw-page-title-main">Xiao-Gang Wen</span> Chinese-American physicist

Xiao-Gang Wen is a Chinese-American physicist. He is a Cecil and Ida Green Professor of Physics at the Massachusetts Institute of Technology and Distinguished Visiting Research Chair at the Perimeter Institute for Theoretical Physics. His expertise is in condensed matter theory in strongly correlated electronic systems. In Oct. 2016, he was awarded the Oliver E. Buckley Condensed Matter Prize.

The toric code is a topological quantum error correcting code, and an example of a stabilizer code, defined on a two-dimensional spin lattice. It is the simplest and most well studied of the quantum double models. It is also the simplest example of topological order—Z2 topological order (first studied in the context of Z2 spin liquid in 1991). The toric code can also be considered to be a Z2 lattice gauge theory in a particular limit. It was introduced by Alexei Kitaev.

<span class="mw-page-title-main">Piers Coleman</span> British-American physicist

Piers Coleman is a British-born theoretical physicist, working in the field of theoretical condensed matter physics. Coleman is professor of physics at Rutgers University in New Jersey and at Royal Holloway, University of London.

In condensed matter physics, a quantum spin liquid is a phase of matter that can be formed by interacting quantum spins in certain magnetic materials. Quantum spin liquids (QSL) are generally characterized by their long-range quantum entanglement, fractionalized excitations, and absence of ordinary magnetic order.

In theoretical physics, anti-de Sitter/condensed matter theory correspondence is the program to apply string theory to condensed matter theory using the AdS/CFT correspondence.

Ashvin Vishwanath is an Indian-American theoretical physicist known for important contributions to condensed matter physics. He is a professor of physics at Harvard University.

<span class="mw-page-title-main">Thomas Maurice Rice</span> Theoretical physicist and professor

Thomas Maurice Rice, known professionally as Maurice Rice, is an Irish theoretical physicist specializing in condensed matter physics.

In condensed matter physics and black hole physics, the Sachdev–Ye–Kitaev (SYK) model is an exactly solvable model initially proposed by Subir Sachdev and Jinwu Ye, and later modified by Alexei Kitaev to the present commonly used form. The model is believed to bring insights into the understanding of strongly correlated materials and it also has a close relation with the discrete model of AdS/CFT. Many condensed matter systems, such as quantum dot coupled to topological superconducting wires, graphene flake with irregular boundary, and kagome optical lattice with impurities, are proposed to be modeled by it. Some variants of the model are amenable to digital quantum simulation, with pioneering experiments implemented in nuclear magnetic resonance.

GrigoryEfimovich Volovik is a Russian theoretical physicist, who specializes in condensed matter physics. He is known for the Volovik effect.

References

  1. ↑ "Subir Sachdev. Herchel Smith Professor of Physics, Harvard University". Official website.
  2. ↑ "Annual Review of Condensed Matter Physics, Planning Editorial Committee – Volume 8, 2017". Annual Reviews Directory. Retrieved 14 September 2021.
  3. ↑ "Annual Review of Condensed Matter Physics, Planning Editorial Committee – Volume 10, 2019". Annual Reviews Directory. Retrieved 14 September 2021.
  4. ↑ "New 2019 Academy Members Announced". 17 April 2019.
  5. ↑ "IAS honorary fellows".
  6. ↑ "INSA Foreign Fellows elected".
  7. ↑ "ICTP – Dirac Medallists 2018". www.ictp.it.
  8. ↑ "2018 Lars Onsager Prize Recipient".
  9. ↑ "Dirac Medal awarded to Professor Subir Sachdev".
  10. ↑ "Subir Sachdev NAS member".
  11. 1 2 3 Sachdev, Subir (1999). Quantum phase transitions . Cambridge University Press. ISBN   0-521-00454-3.
  12. ↑ "Condensed matter physicist Subir Sachdev to deliver Salam Distinguished Lectures 2014".
  13. ↑ "Lorentz Chair".
  14. ↑ "Nine Leading Researchers Join Stephen Hawking as Distinguished Research Chairs at PI". Perimeter Institute for Theoretical Physics.
  15. ↑ "All Fellows – John Simon Guggenheim Memorial Foundation". John Simon Guggenheim Memorial Foundation. Retrieved 26 January 2010.
  16. ↑ "APS Fellow archive". APS. Retrieved 21 September 2020.
  17. ↑ "Past Fellows". sloan.org. Retrieved 23 October 2018.
  18. ↑ "LeRoy Apker Award Recipient". American Physical Society. Retrieved 30 June 2010.
  19. ↑ "Subir Sachdev, Perimeter Institute".
  20. ↑ "Endowment Chairs at TIFR".
  21. ↑ "Infosys Prize – Jury 2020". www.infosys-science-foundation.com. Retrieved 10 December 2020.
  22. 1 2 Sachdev, Subir; Ye, Jinwu (24 May 1993). "Gapless spin-fluid ground state in a random quantum Heisenberg magnet". Physical Review Letters. 70 (21): 3339–3342. arXiv: cond-mat/9212030 . Bibcode:1993PhRvL..70.3339S. doi:10.1103/PhysRevLett.70.3339. ISSN   0031-9007. PMID   10053843.
  23. ↑ Patel, Aavishkar A.; Guo, Haoyu; Esterlis, Ilya; Sachdev, Subir (18 August 2023). "Universal theory of strange metals from spatially random interactions". Science. 381 (6659): 790–793. arXiv: 2203.04990 . Bibcode:2023Sci...381..790P. doi:10.1126/science.abq6011. ISSN   0036-8075. PMID   37590350.
  24. 1 2 Sachdev, Subir (4 October 2010). "Holographic Metals and the Fractionalized Fermi Liquid". Physical Review Letters. 105 (15): 151602. arXiv: 1006.3794 . Bibcode:2010PhRvL.105o1602S. doi:10.1103/PhysRevLett.105.151602. ISSN   0031-9007. PMID   21230891.
  25. ↑ Damle, Kedar; Sachdev, Subir (1 October 1997). "Nonzero-temperature transport near quantum critical points". Physical Review B. 56 (14): 8714–8733. arXiv: cond-mat/9705206 . Bibcode:1997PhRvB..56.8714D. doi:10.1103/PhysRevB.56.8714. ISSN   0163-1829.
  26. ↑ Sachdev, Subir (13 November 2015). "Bekenstein-Hawking Entropy and Strange Metals". Physical Review X. 5 (4): 041025. arXiv: 1506.05111 . Bibcode:2015PhRvX...5d1025S. doi:10.1103/PhysRevX.5.041025. ISSN   2160-3308.
  27. ↑ Chowdhury, Debanjan; Georges, Antoine; Parcollet, Olivier; Sachdev, Subir (14 September 2022). "Sachdev-Ye-Kitaev models and beyond: Window into non-Fermi liquids". Reviews of Modern Physics. 94 (3): 035004. arXiv: 2109.05037 . Bibcode:2022RvMP...94c5004C. doi:10.1103/RevModPhys.94.035004. ISSN   0034-6861.
  28. ↑ Maldacena, Juan; Shenker, Stephen H.; Stanford, Douglas (2016). "A bound on chaos". Journal of High Energy Physics. 2016 (8): 106. arXiv: 1503.01409 . Bibcode:2016JHEP...08..106M. doi:10.1007/JHEP08(2016)106. ISSN   1029-8479. S2CID   84832638.
  29. ↑ Dray, Tevian; 't Hooft, Gerard (1985). "The gravitational shock wave of a massless particle". Nuclear Physics B. 253: 173–188. Bibcode:1985NuPhB.253..173D. doi:10.1016/0550-3213(85)90525-5. hdl: 1874/4758 . ISSN   0550-3213.
  30. ↑ Shenker, Stephen H.; Stanford, Douglas (2014). "Black holes and the butterfly effect". Journal of High Energy Physics. 2014 (3): 67. arXiv: 1306.0622 . Bibcode:2014JHEP...03..067S. doi:10.1007/JHEP03(2014)067. ISSN   1029-8479. S2CID   54184366.
  31. ↑ Georges, A.; Parcollet, O.; Sachdev, S. (1 March 2001). "Quantum fluctuations of a nearly critical Heisenberg spin glass". Physical Review B. 63 (13): 134406. arXiv: cond-mat/0009388 . Bibcode:2001PhRvB..63m4406G. doi:10.1103/PhysRevB.63.134406. ISSN   0163-1829.
  32. ↑ Müller, Markus; Sachdev, Subir (19 September 2008). "Collective cyclotron motion of the relativistic plasma in graphene". Physical Review B. 78 (11): 115419. arXiv: 0801.2970 . Bibcode:2008PhRvB..78k5419M. doi:10.1103/PhysRevB.78.115419. ISSN   1098-0121.
  33. ↑ Patel, Aavishkar A.; Guo, Haoyu; Esterlis, Ilya; Sachdev, Subir (18 August 2023). "Universal theory of strange metals from spatially random interactions". Science. 381 (6659): 790–793. arXiv: 2203.04990 . Bibcode:2023Sci...381..790P. doi:10.1126/science.abq6011. ISSN   0036-8075. PMID   37590350.
  34. ↑ Bandurin, D. A.; Torre, I.; Kumar, R. K.; Ben Shalom, M.; Tomadin, A.; Principi, A.; Auton, G. H.; Khestanova, E.; Novoselov, K. S.; Grigorieva, I. V.; Ponomarenko, L. A.; Geim, A. K.; Polini, M. (2016). "Negative local resistance caused by viscous electron backflow in graphene". Science. 351 (6277): 1055–1058. arXiv: 1509.04165 . Bibcode:2016Sci...351.1055B. doi:10.1126/science.aad0201. ISSN   0036-8075. PMID   26912363. S2CID   45538235.
  35. ↑ Crossno, Jesse; Shi, Jing K.; Wang, Ke; Liu, Xiaomeng; Harzheim, Achim; Lucas, Andrew; Sachdev, Subir; Kim, Philip; Taniguchi, Takashi; Watanabe, Kenji; Ohki, Thomas A.; Fong, Kin Chung (4 March 2016). "Observation of the Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene". Science. 351 (6277): 1058–1061. arXiv: 1509.04713 . Bibcode:2016Sci...351.1058C. doi:10.1126/science.aad0343. ISSN   0036-8075. PMID   26912362.
  36. ↑ Michon, Bastien; Berthod, Christophe; Rischau, Carl Willem; Ataei, Amirreza; Chen, Lu; Komiya, Seiki; Ono, Shimpei; Taillefer, Louis; van der Marel, Dirk; Georges, Antoine (26 May 2023). "Reconciling scaling of the optical conductivity of cuprate superconductors with Planckian resistivity and specific heat". Nature Communications. 14 (1): 3033. arXiv: 2205.04030 . Bibcode:2023NatCo..14.3033M. doi:10.1038/s41467-023-38762-5. ISSN   2041-1723. PMC   10220041 . PMID   37236962.
  37. ↑ Iliesiu, Luca V.; Murthy, Sameer; Turiaci, Gustavo J. (2022). "Revisiting the Logarithmic Corrections to the Black Hole Entropy". arXiv: 2209.13608 [hep-th].
  38. ↑ Sachdev, Subir (2023). "Quantum statistical mechanics of the Sachdev-Ye-Kitaev model and charged black holes". arXiv: 2304.13744 [cond-mat.str-el].
  39. ↑ Bousso, Raphael; Dong, Xi; Engelhardt, Netta; Faulkner, Thomas; Hartman, Thomas; Shenker, Stephen H.; Stanford, Douglas (2022). "Snowmass White Paper: Quantum Aspects of Black Holes and the Emergence of Spacetime". arXiv: 2201.03096 .{{cite journal}}: Cite journal requires |journal= (help)
  40. ↑ Anderson, P.W. (1973). "Resonating valence bonds: A new kind of insulator?". Materials Research Bulletin. 8 (2): 153–160. doi:10.1016/0025-5408(73)90167-0. ISSN   0025-5408.
  41. ↑ Read, N.; Sachdev, Subir (1991). "Large-Nexpansion for frustrated quantum antiferromagnets". Physical Review Letters. 66 (13): 1773–1776. Bibcode:1991PhRvL..66.1773R. doi:10.1103/PhysRevLett.66.1773. ISSN   0031-9007. PMID   10043303.
  42. ↑ Wen, X. G. (1991). "Mean-field theory of spin-liquid states with finite energy gap and topological orders". Physical Review B. 44 (6): 2664–2672. Bibcode:1991PhRvB..44.2664W. doi:10.1103/PhysRevB.44.2664. ISSN   0163-1829. PMID   9999836.
  43. ↑ Jalabert, Rodolfo A.; Sachdev, Subir (1991). "Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model". Physical Review B. 44 (2): 686–690. Bibcode:1991PhRvB..44..686J. doi:10.1103/PhysRevB.44.686. ISSN   0163-1829. PMID   9999168.
  44. ↑ Sachdev, S.; Vojta, M. (1999). "Translational symmetry breaking in two-dimensional antiferromagnets and superconductors". J. Phys. Soc. Jpn. 69, Supp. B: 1. arXiv: cond-mat/9910231 . Bibcode:1999cond.mat.10231S.
  45. ↑ Sachdev, Subir (2019). "Topological order, emergent gauge fields, and Fermi surface reconstruction". Reports on Progress in Physics. 82 (1): 014001. arXiv: 1801.01125 . Bibcode:2019RPPh...82a4001S. doi:10.1088/1361-6633/aae110. ISSN   0034-4885. PMID   30210062. S2CID   52197314.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.