# Subir Sachdev

Subir Sachdev is Herchel Smith Professor of physics 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, and is Editor-in-Chief of Reports on Progress in Physics 2022-.
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.

## 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 at the Perimeter Institute for Theoretical Physics, and the Dr. Homi J. Bhabha Chair Professorship at the Tata Institute of Fundamental Research. He has been a Visiting Scholar at the Flatiron Institute since 2019, and Miguel Virasoro Visiting International Chair, at the International Centre for Theoretical Physics since 2024. He has also been on the Physical Sciences jury for the Infosys Prize from 2018.

## Research

Sachdev has studied the nature of quantum entanglement in two-dimensional antiferromagnets, introducing several key ideas in a series of papers in 1989-1992. This includes the first proposal in 1990 of a fractionalized spin liquid phase with time-reversal symmetry, the Z$_2$ spin liquid; this was described by an emergent Z$_2$ gauge theory, with the same structure of excitations that appeared later in Kitaev's solvable toric code model. 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 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 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, 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 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)). Sachdev proposed a solvable model of a strange metal (a variant of which is now called the Sachdev–Ye–Kitaev (SYK), which was shown to saturate such a bound on the time to reach quantum chaos.
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)), 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 that the SYK model maps holographically to the low energy physics of charged black holes in 4 spacetime dimension. Also key to this connection were the facts that in the limit of zero temperature, charged black holes have a non-zero entropy proportional to the horizon area, and the SYK model has a non-zero entropy density. Indeed, the SYK model was the first model to exhibit a non-vanishing zero temperature entropy density without an exponentially large ground state degeneracy, and so the holographic mapping implied that charged black holes share this feature.
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.
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 have been connected to experiments on graphene and the cuprate superconductors. 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, and provides the underlying Hamiltonian system upon which advances on the Page curve of entanglement entropy of evaporating black holes have been tested.
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 Z$_2$ quantum spin liquids

Phillip W. Anderson proposed 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 and Wen by the connection to a Z$_2$ gauge theory. Sachdev was also the first to show that the RVB state is an odd Z$_2$ gauge theory,. An odd Z$_2$ spin liquid has a background Z$_2$ 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 Z$_2$ gauge flux (also known as the m sector)). Sachdev showed that antiferromagnets with half-integer spin form odd Z$_2$ spin liquids, and those with integer spin form even Z$_2$ 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 Z$_2$ 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.
Z$_2$ 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.

## Honors

* LeRoy Apker Award Recipient, 1982.
* Alfred P. Sloan Foundation Fellow, February 1989.
* Fellow of the American Physical Society "for his contributions to the theory of quantum phase transitions and its application to correlated electron materials".
* John Simon Guggenheim Memorial Foundation Fellow, 2003.
* Perimeter Institute for Theoretical Physics Distinguished Research Chair, 2009–14.
* Abdus Salam Distinguished Lecturer, International Center for Theoretical Physics, Trieste, Italy, 2014.
* Hendrik Lorentz Chair, Lorentz Institute, 2012.
* Elected to the U.S. National Academy of Sciences, 2014. Citation:
   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, is the basic text of the field.
* Dirac Medal for the Advancement of Theoretical Physics (University of New South Wales), 2015. Citation:
   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.
* Lars Onsager Prize (American Physical Society), 2018, to recognize outstanding research in theoretical statistical physics including the quantum fluids. Citation:
   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.
* Dirac Medal (International Center for Theoretical Physics), 2018; shared with Dam Thanh Son and Xiao-Gang Wen for "independent contributions towards understanding novel phases in strongly interacting many-body systems, introducing original transdisciplinary techniques". Citation:
   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.
* Foreign Fellow of the Indian National Science Academy, 2019. Citation:
   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.
* Elected to the American Academy of Arts and Sciences, 2019.
* Honorary Fellow of the Indian Academy of Sciences, 2019.
* Jacques Solvay International Chair in Physics, International Solvay Institutes, Brussels, 2023
* Raman Chair, Indian Academy of Sciences, 2023-24.
* Foreign Member of the Royal Society, 2023. Citation:
   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.

## Books

* Sachdev, Subir (7 April 2011). Quantum Phase Transitions. Cambridge University Press. ISBN 978-1-139-50021-0.
* Hartnoll, Sean A.; Lucas, Andrew; Sachdev, Subir (16 March 2018). Holographic Quantum Matter. MIT Press. ISBN 978-0-262-34802-7.
* Sachdev, Subir (13 April 2023). Quantum Phases of Matter. Cambridge University Press. ISBN 978-1-009-21269-4.