Contributor info: Dr Anushya Chandran

David M. Long, Dominik Hahn, Marin Bukov, Anushya Chandran

SciPost Phys. 15, 251 (2023) · published 22 December 2023 | Toggle abstract · pdf

Many problems in quantum dynamics can be cast as the decay of a single quantum state into a continuum. The time-dependent overlap with the initial state, called the fidelity, characterizes this decay. We derive an analytic expression for the fidelity after a quench to an ergodic Hamiltonian. The expression is valid for both weak and strong quenches, and timescales before finiteness of the Hilbert space limits the fidelity. It reproduces initial quadratic decay and asymptotic exponential decay with a rate which, for strong quenches, differs from Fermi's golden rule. The analysis relies on the statistical Jacobi approximation (SJA), which was originally applied in nearly localized systems, and which we here adapt to well-thermalizing systems. Our results demonstrate that the SJA is predictive in disparate regimes of quantum dynamics.

Long-Hin Tang, David M. Long, Anatoli Polkovnikov, Anushya Chandran, Pieter W. Claeys

SciPost Phys. 15, 030 (2023) · published 26 July 2023 | Toggle abstract · pdf

Central spin models provide an idealized description of interactions between a central degree of freedom and a mesoscopic environment of surrounding spins. We show that the family of models with a spin-1 at the center and XX interactions of arbitrary strength with surrounding spins is integrable. Specifically, we derive an extensive set of conserved quantities and obtain the exact eigenstates using the Bethe ansatz. As in the homogenous limit, the states divide into two exponentially large classes: bright states, in which the spin-1 is entangled with its surroundings, and dark states, in which it is not. On resonance, the bright states further break up into two classes depending on their weight on states with central spin polarization zero. These classes are probed in quench dynamics wherein they prevent the central spin from reaching thermal equilibrium. In the single spin-flip sector we explicitly construct the bright states and show that the central spin exhibits oscillatory dynamics as a consequence of the semilocalization of these eigenstates. We relate the integrability to the closely related class of integrable Richardson-Gaudin models, and conjecture that the spin-$s$ central spin XX model is integrable for any $s$.

Philip J D Crowley, Anushya Chandran

SciPost Phys. 12, 201 (2022) · published 24 June 2022 | Toggle abstract · pdf

The many-body localised (MBL) to thermal crossover observed in exact diagonalisation studies remains poorly understood as the accessible system sizes are too small to be in an asymptotic scaling regime. We develop a model of the crossover in short 1D chains in which the MBL phase is destabilised by the formation of many-body resonances. The model reproduces several properties of the numerically observed crossover, including an apparent correlation length exponent $\nu=1$, exponential growth of the Thouless time with disorder strength, linear drift of the critical disorder strength with system size, scale-free resonances, apparent $1/\omega$ dependence of disorder-averaged spectral functions, and sub-thermal entanglement entropy of small subsystems. In the crossover, resonances induced by a local perturbation are rare at numerically accessible system sizes $L$ which are smaller than a \emph{resonance length} $\lambda$. For $L \gg \sqrt{\lambda}$ (in lattice units), resonances typically overlap, and this model does not describe the asymptotic transition. The model further reproduces controversial numerical observations which Refs. [Suntajs et al 2019, Sels & Polkovnikov 2020] claimed to be inconsistent with MBL. We thus argue that the numerics to date is consistent with a MBL phase in the thermodynamic limit.

Philip J. D. Crowley, Anushya Chandran

SciPost Phys. 12, 103 (2022) · published 23 March 2022 | Toggle abstract · pdf

The eigenstate thermalisation hypothesis (ETH) is a statistical characterisation of eigen-energies, eigenstates and matrix elements of local operators in thermalising quantum systems. We develop an ETH-like ansatz of a partially thermalising system composed of a spin-1/2 coupled to a finite quantum bath. The spin-bath coupling is sufficiently weak that ETH does not apply, but sufficiently strong that perturbation theory fails. We calculate (i) the distribution of fidelity susceptibilities, which takes a broadly distributed form, (ii) the distribution of spin eigenstate entropies, which takes a bi-modal form, (iii) infinite time memory of spin observables, (iv) the distribution of matrix elements of local operators on the bath, which is non-Gaussian, and (v) the intermediate entropic enhancement of the bath, which interpolates smoothly between zero and the ETH value of log 2. The enhancement is a consequence of rare many-body resonances, and is asymptotically larger than the typical eigenstate entanglement entropy. We verify these results numerically and discuss their connections to the many-body localisation transition.