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Strange metals and black holes: insights from the Sachdev-Ye-Kitaev model
No full textComplex many-particle quantum entanglement is a central theme in two distinct
major topics in physics: the strange metal state found in numerous correlated
electron compounds, and the quantum theory of black holes in Einstein gravity.
The Sachdev-Ye-Kitaev model provides a solvable theory of entangled
many-particle quantum states without quasiparticle excitations. This article
reviews how this toy model has led to realistic universal models of strange
metals, and to new insights on the quantum states of black holes.Comment: 31 pages, 11 figures; Some of the introductory discussion in this
article overlaps with the review in arXiv:2205.02285; companion article on
black holes is arXiv:2304.1374
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The Sachdev-Ye-Kitaev Model and Matter Without Quasiparticles
No full textThis thesis is devoted to the study of Sachdev-Ye-Kitaev (SYK) models, which describe matter without quasiparticles. The SYK model is an exactly solvable model that is hoped to bring insights into the understanding of strongly correlated materials.
The main part discusses different aspects of SYK models. Chapter 2 presents numerical studies of the SYK models, shows its non-Fermi liquid nature and verifies the analytical predictions on two-point function and thermal entropies. Chapter 3 considers the thermodynamic and transport properties of the complex SYK models in higher dimensional generalizations, we show some universal relations obtained from SYK models which are consistent with holographic theories. Chapter 4 discusses a supersymmetric generalization of the SYK model. We show a different a scaling from the normal SYK model both analytically and numerically. We also discuss a different origin of the extensive zero temperature entropy in theory. Chapter 5 considers a continuous set of boson-fermion SYK models with a tunable low-energy scaling dimension. From the explicit computation of out of time ordered correlators, we find the theory is less chaotic in the free fermion limit. Chapter 6 describes the phases of a solvable - model of electrons with an SYK-like form. We find a fractionalization picture where the deconfined phase is similar to the pseudo gap regime of underdoped cuprates, while the `quasi-Higgs' phase is similar to the metallic phase of overdoped cuprates.Physic
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Quantum Quench of the Sachdev-Ye-Kitaev Model
No full textWe describe the nonequilibrium quench dynamics of the Sachdev-Ye-Kitaev models of fermions with random all-to-all interactions. These provide tractable models of the dynamics of quantum systems without quasiparticle excitations. The Kadanoff-Baym equations show that, at long times, the fermion two-point function has a thermal form at a final temperature determined by energy conservation, and the numerical analysis is consistent with a thermalization rate proportional to this temperature. We also obtain an exact analytic solution of the quench dynamics in the large q limit of a model with q fermion interactions: in this limit, the thermalization of the two-point function is instantaneous.Accepted Manuscrip
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Supersymmetric Sachdev-Ye-Kitaev models
No full textWe discuss a supersymmetric generalization of the Sachdev-Ye-Kitaev model. These are quantum mechanical models involving N Majorana fermions. The supercharge is given by a polynomial expression in terms of the Majorana fermions with random coefficients. The Hamiltonian is the square of the supercharge. The =1 model with a single supercharge has unbroken supersymmetry at large N, but non-perturbatively spontaneously broken supersymmetry in the exact theory. We analyze the model by looking at the large N equation, and also by performing numerical computations for small values of N. We also compute the large N spectrum of "singlet" operators, where we find a structure qualitatively similar to the ordinary SYK model. We also discuss an =2 version. In this case, the model preserves supersymmetry in the exact theory and we can compute a suitably weighted Witten index to count the number of ground states, which agrees with the large N computation of the entropy. In both cases, we discuss the supersymmetric generalizations of the Schwarzian action which give the dominant effects at low energies.PhysicsVersion of Recor
Spin liquid to spin glass crossover in the random quantum Heisenberg magnet
No full textWe study quantum SU() spins with all-to-all and random Heisenberg exchange interactions of root-mean-square strength . The model has a spin liquid ground state with the spinons obeying the equations of the Sachdev-Ye-Kitaev (SYK) model. Numerical studies of the SU(2) model with spins show spin glass order in the ground state, but also display SYK spin liquid behavior in the intermediate frequency spin spectrum. We employ a expansion to describe the crossover from fractionalized fermionic spinons to a confining spin glass state with weak spin glass order . The SYK spin liquid behavior persists down to a frequency , and for \omega < \omega_\ast, the spectral density is linear in , thus quenching the extensive zero temperature entropy of the spin liquid. The linear spectrum is qualitatively similar to that obtained earlier using bosonic spinons for large . We argue that the extensive SYK spin liquid entropy is transformed as to an extensive complexity of the spin glass state
Theory of a Planckian Metal
No full textSachdev, Subir. (2019). Theory of a Planckian Metal. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/203651
Quantum statistical mechanics of the Sachdev-Ye-Kitaev model and charged black holes
No full textThis review is a contribution to a book dedicated to the memory of Michael E. Fisher. The first example of a quantum many body system not expected to have any quasiparticle excitations was the Wilson-Fisher conformal field theory. The absence of quasiparticles can be established in the compressible, metallic state of the Sachdev-Ye-Kitaev model of fermions with random interactions. The solvability of the latter model has enabled numerous computations of the non-quasiparticle dynamics of chaotic many-body states, such as those expected to describe quantum black holes. We review thermodynamic properties of the SYK model, and describe how they have led to an understanding of the universal structure of the low energy density of states of charged black holes without low energy supersymmetry.28 pages, 10 figures; Published in 50 years of the renormalization group , https://doi.org/10.1142/13571 , dedicated to the memory of Michael E. Fisher, edited by Amnon Aharony, Ora Entin-Wohlman, David Huse, and Leo Radzihovsky, World Scientific; companion article on strange metals is arXiv:2305.0100
Theory of a Planckian metal
No full textSachdev, Subir. (2019). Theory of a Planckian metal. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/203395
Is the incidence of dementia declining?
No full textAction on preventative health could lower the risk of dementia for future generations, argues this report.
Executive summary
The world-wide projections of the prevalence of dementia in the coming decades have been a source of great concern to health systems and societies around the world. The World Alzheimer Report 2010 estimated that there were 36 million people with dementia in 2010, with an expected doubling every 20 years to nearly 115 million in 2050. These sobering figures are based on assumptions that the age-adjusted prevalence of dementia would remain constant and the population would continue to age at the current rate.
The assumption that the incidence of dementia will remain stable is now being put into question. There is emerging evidence to suggest that the incidence of dementia in older individuals may be declining. It appears that this change may be recent and has possibly occurred only in the last one to two decades. It may also be restricted so far to high income countries, although data from low and middle income countries are lacking.
The reasons for this change are not understood, but education, more stimulating environments and better control of vascular risk factors may have contributed. The data are still preliminary and more studies are needed to establish the extent of this change and understand its causes. It should be noted that the decline is not large enough to offset the increase in prevalence of dementia due to the ageing of the population and therefore investment and efforts to develop better treatments and care for people with dementia need to continue.
The fact that dementia rates are malleable is an encouraging finding but the reduction cannot be taken for granted as gains in population health can easily be lost if societies do not remain vigilant and continually proactive. These preliminary findings provide a strong argument for large scale Government investment in dementia-prevention strategies, which should start from early life
Space-Time in the Sachdev-Ye-Kitaev Model
No full textThe question of the bulk space-time in the Sachdev-Ye-Kitaev model will be discussed . Starting with the basic issue regarding its signature a bi-local map will be described to reach the bulk. Physical properties of the SYK spectrum will
be discussed.Jevicki, Antal. (2018). Space-Time in the Sachdev-Ye-Kitaev Model. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/197529
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