New characteristic of quantum many-body chaotic systems

Dymarsky, Anatoly; Liu, Hong

doi:10.1103/physreve.99.010102

Cited by 31 publications

(28 citation statements)

References 26 publications

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“…Indeed, in energy windows ω E Th where E Th is set by a scale called the Thouless energy, f A (E, ω) is constant (although this can be subtle in systems with diffusive transport [66]). Such behavior in the off-diagonal matrix elements has been observed numerically [64,67,68]. Then it is consistent with k-invariance that in small energy windows (and thus at late time scales) ETH predicts decoupled forms of correlation functions.…”

Section: Consider Asupporting

confidence: 80%

Spectral decoupling in many-body quantum chaos

Cotler

Hunter-Jones

2020

J. High Energ. Phys.

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We argue that in a large class of disordered quantum many-body systems, the late time dynamics of time-dependent correlation functions is captured by random matrix theory, specifically the energy eigenvalue statistics of the corresponding ensemble of disordered Hamiltonians. We find that late time correlation functions approximately factorize into a time-dependent piece, which only depends on spectral statistics of the Hamiltonian ensemble, and a time-independent piece, which only depends on the data of the constituent operators of the correlation function. We call this phenomenon “spectral decoupling”, which signifies a dynamical onset of random matrix theory in correlation functions. A key diagnostic of spectral decoupling is k-invariance, which we refine and study in detail. Particular emphasis is placed on the role of symmetries, and connections between k-invariance, scrambling, and OTOCs. Disordered Pauli spin systems, as well as the SYK model and its variants, provide a rich source of disordered quantum many-body systems with varied symmetries, and we study k-invariance in these models with a combination of analytics and numerics.

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Section: Consider Asupporting

confidence: 80%

Spectral decoupling in many-body quantum chaos

Cotler

Hunter-Jones

2020

J. High Energ. Phys.

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“…This is essentially the underlying reason for the non-relativistic axion-dilaton theory at large n and fixed g YM . However, we see that if we keep g 2 YM n fixed then the hypermultiplet and W-boson have a fixed nonzero mass while the magnetically charged particles decouple. Also any possible multi-particle states made out of the hypermultiplets and W-boson survive the limit of fixed g 2 YM n. At small λ the physics is rather complicated since the electric BPS particles are light.…”

Section: Jhep04(2021)214mentioning

confidence: 89%

“…In fact some of the earliest work on ETH already made contact with Random Matrix Theory. For some recent work see for instance [1,2] and references therein.) Here we are studying matrix elements of O 1 between…”

Section: Jhep04(2021)214mentioning

confidence: 99%

Extremal correlators and random matrix theory

Grassi

Komargodski

Tizzano

2021

J. High Energ. Phys.

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We study the correlation functions of Coulomb branch operators of four-dimensional $$ \mathcal{N} $$ N = 2 Superconformal Field Theories (SCFTs). We focus on rank-one theories, such as the SU(2) gauge theory with four fundamental hypermultiplets. “Extremal” correlation functions, involving exactly one anti-chiral operator, are perhaps the simplest nontrivial correlation functions in four-dimensional Quantum Field Theory. We show that the large charge limit of extremal correlators is captured by a “dual” description which is a chiral random matrix model of the Wishart-Laguerre type. This gives an analytic handle on the physics in some particular excited states. In the limit of large random matrices we find the physics of a non-relativistic axion-dilaton effective theory. The random matrix model also admits a ’t Hooft expansion in which the matrix is taken to be large and simultaneously the coupling is taken to zero. This explains why the extremal correlators of SU(2) gauge theory obey a nontrivial double scaling limit in states of large charge. We give an exact solution for the first two orders in the ’t Hooft expansion of the random matrix model and compare with expectations from effective field theory, previous weak coupling results, and we analyze the non-perturbative terms in the strong ’t Hooft coupling limit. Finally, we apply the random matrix theory techniques to study extremal correlators in rank-1 Argyres-Douglas theories. We compare our results with effective field theory and with some available numerical bootstrap bounds.

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“…Interestingly, it was recently observed that the function |f (�)| 2 can be defined and remains smooth even in generic integrable systems 72 . Then |f (�)| 2 vanishes as → 0 for deformations of the Hamiltonian along integrable directions 44,[73][74][75] .…”

Section: Persistent Dark States Away From the Integrable Lines Inmentioning

confidence: 99%

Persistent dark states in anisotropic central spin models

Villazon

Claeys

Pandey

et al. 2020

Sci Rep

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Long-lived dark states, in which an experimentally accessible qubit is not in thermal equilibrium with a surrounding spin bath, are pervasive in solid-state systems. We explain the ubiquity of dark states in a large class of inhomogeneous central spin models using the proximity to integrable lines with exact dark eigenstates. At numerically accessible sizes, dark states persist as eigenstates at large deviations from integrability, and the qubit retains memory of its initial polarization at long times. Although the eigenstates of the system are chaotic, exhibiting exponential sensitivity to small perturbations, they do not satisfy the eigenstate thermalization hypothesis. Rather, we predict long relaxation times that increase exponentially with system size. We propose that this intermediate chaotic but non-ergodic regime characterizes mesoscopic quantum dot and diamond defect systems, as we see no numerical tendency towards conventional thermalization with a finite relaxation time.

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New characteristic of quantum many-body chaotic systems

Cited by 31 publications

References 26 publications

Spectral decoupling in many-body quantum chaos

Spectral decoupling in many-body quantum chaos

Extremal correlators and random matrix theory

Persistent dark states in anisotropic central spin models

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