Far-from-Equilibrium Spin Transport in Heisenberg Quantum Magnets

We study relaxation times, also called mixing times, of quantum many-body systems described by a Lindblad master equation. We in particular study the scaling of the spectral gap with the system length, the so-called dynamical exponent, identifying a number of transitions in the scaling. For systems with bulk dissipation we generically observe different scaling for small and for strong dissipation strength, with a critical transition strength going to zero in the thermodynamic limit. We also study a related phase transition in the largest decay mode. For systems with only boundary dissipation we show a generic bound that the gap can not be larger than ∼ 1/L. In integrable systems with boundary dissipation one typically observes scaling ∼ 1/L 3 , while in chaotic ones one can have faster relaxation with the gap scaling as ∼ 1/L and thus saturating the generic bound. We also observe transition from exponential to algebraic gap in systems with localized modes.

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“…Refs. [31,32], with individual components like few qubit controlled dissipation [33] or Heisenberg spin chains [34,35] already demonstrated.…”

Section: Lindblad Equationmentioning

confidence: 99%

Relaxation times of dissipative many-body quantum systems

2015

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“…Concerning the relevance of the interacting Luttinger model, before closing the section, we would like to mention that only recently pioneering experiments in ultra-cold gases both in and out of equilibrium explored the transient and prethermalization dynamics of systems [16][17][18][19][20][21][22][23][24][25][26][68][69][70] effectively described by a quadratic Luttinger model, the bosonic theory of the Hamiltonian in Eq. (2.2).…”

Section: Interacting Luttinger Liquidmentioning

confidence: 99%

“…The increasing number of cold atom experiments performed under out of equilibrium conditions [14][15][16][17][18][19][20][21][22][23] has driven significant interest in the theoretical understanding of the non-equilibrium dynamics in quantum many-body systems. Importantly, these experiments share a remarkable isolation from the environment, thereby probing the purely coherent unitary time evolution on the experimentally relevant time scales.…”

Section: Introductionmentioning

confidence: 99%

Prethermalization and thermalization of a quenched interacting Luttinger liquid

2016

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We study the relaxation dynamics of interacting, one-dimensional fermions with band curvature after a weak quench in the interaction parameter at zero temperature. Our model lies within the class of interacting Luttinger Liquids, where the harmonic Luttinger theory is extended by a weak integrability breaking phonon scattering term. In order to solve for the non-equilibrium time evolution, we use quantum kinetic equations exploiting the resonant but subleading character of the phonon interaction term. The interplay between phonon scattering and the quadratic Luttinger theory leads to the emergence of three distinct spatio-temporal regimes for the fermionic real-space correlation function. It features the crossover from a prequench to a prethermal state, finally evolving towards a thermal state on increasing length and time scales. The characteristic algebraically decaying real-space correlations in the prethermalized regime become modulated by an amplitude, which is decaying in time according to a stretched-exponential as an effect of the interactions. The asymptotic thermalization dynamics is governed by energy transport over large distances from the thermalized to the non-thermalized regions via macroscopic, dynamical slow modes. This is revealed in an algebraic decay of the system's effective temperature. The numerical value of the associated exponent agrees with the dynamical critical exponent of the Kardar-Parisi-Zhang universality class. We also discuss a criterion for the applicability of this theory away from the integrable limit of non-interacting fermions.

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“…In the spirit of quantum quenches [9], which are typically implemented in cold-atom setups [10][11][12], energy transport in one-dimensional quantum many-body systems can be addressed by means of the following partitioning protocol [13][14][15][16]. Two (ideally semi-infinite) chains are prepared in thermal equilibrium with different temperatures (see the sketch in Fig.…”

Section: Introductionmentioning

confidence: 99%

Energy transport between two integrable spin chains

et al. 2016

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We study the energy transport in a system of two half-infinite XXZ chains initially kept separated at different temperatures, and later connected and let free to evolve unitarily. By changing independently the parameters of the two halves, we highlight, through bosonisation and time-dependent matrix-product-state simulations, the different contributions of low-lying bosonic modes and of fermionic quasi-particles to the energy transport. In the simulations we also observe that the energy current reaches a finite value which only slowly decays to zero. The general pictures that emerges is the following. Since integrability is only locally broken in this model, a pre-equilibration behaviour may appear. In particular, when the sound velocities of the bosonic modes of the two halves match, the low-temperature energy current is almost stationary and described by a formula with a nonuniversal prefactor interpreted as a transmission coefficient. Thermalisation, characterized by the absence of any energy flow, occurs only on longer time-scales which are not accessible with our numerics.

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Far-from-Equilibrium Spin Transport in Heisenberg Quantum Magnets

Cited by 223 publications

References 55 publications

Relaxation times of dissipative many-body quantum systems

Relaxation times of dissipative many-body quantum systems

Prethermalization and thermalization of a quenched interacting Luttinger liquid

Energy transport between two integrable spin chains

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