High-temperature coherent transport in the XXZ chain in the presence of an impurity

Brenes, Marlon; Mascarenhas, Eduardo; Rigol, Marcos; Goold, John

doi:10.1103/physrevb.98.235128

Cited by 64 publications

(77 citation statements)

References 76 publications

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“…Recently, a large number of studies addressed the influence of integrability-breaking static impurities on quantum ergodicity and thermalization (see, e.g., Refs. [70][71][72][73][74]), and showed that an O(1) integrability-breaking term is enough to induce quantum-chaotic statistics of energy levels [75][76][77][78][79]. Here, we provide numerical evidence that an O(1)-integrability-breaking term, introduced by an itinerant electron coupled to noninteracting phonons, is sufficient to observe perfect ETH properties of all Hamiltonian eigenstates in the bulk of the spectrum.…”

Section: Introductionmentioning

confidence: 63%

Eigenstate thermalization and quantum chaos in the Holstein polaron model

et al. 2019

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The eigenstate thermalization hypothesis (ETH) is a successful theory that provides sufficient criteria for ergodicity in quantum many-body systems. Most studies were carried out for Hamiltonians relevant for ultracold quantum gases and single-component systems of spins, fermions, or bosons. The paradigmatic example for thermalization in solid-state physics are phonons serving as a bath for electrons. This situation is often viewed from an open-quantum system perspective. Here, we ask whether a minimal microscopic model for electron-phonon coupling is quantum chaotic and whether it obeys ETH, if viewed as a closed quantum system. Using exact diagonalization, we address this question in the framework of the Holstein polaron model. Even though the model describes only a single itinerant electron, whose coupling to dispersionless phonons is the only integrability-breaking term, we find that the spectral statistics and the structure of Hamiltonian eigenstates exhibit essential properties of the corresponding random-matrix ensemble. Moreover, we verify the ETH ansatz both for diagonal and offdiagonal matrix elements of typical phonon and electron observables, and show that the ratio of their variances equals the value predicted from random-matrix theory.

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Section: Introductionmentioning

confidence: 63%

Eigenstate thermalization and quantum chaos in the Holstein polaron model

et al. 2019

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“…We conclude by stating that systems where integrability is broken only in a finite region of space are therefore special, even though they look non-integrable under conventional indicators such as the level spacing statistics [27,29]. This demands a novel characterisation of integrability (or the lack thereof) appropriate for inhomogeneous settings.…”

Section: Resultsmentioning

confidence: 93%

“…Yet, ballistic transport (a consequence of integrability) is supported in each separate half of the chain. In general, the community is currently considering the presence of forms of local integrability breaking terms, such as localized defects [27,29,42,[54][55][56]; our work fits within this research effort.…”

Section: Resultsmentioning

confidence: 98%

“…Groundbreaking cold-atom experiments have also investigated several aspects of the coherent dynamics of closed quantum many-body systems [16][17][18][19][20][21][22][23][24]. These research efforts allowed to faithfully address how the presence of impurities and inhomogeneities may affect the quantum transport phenomena, also far from the linearresponse regime [25][26][27][28][29].As a paradigmatic example, we study a setup composed of two different semi-infinite spin-1/2 chains connected through a junction at x = 0 (see Fig. 1) [27].…”

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confidence: 99%

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Ballistic transport and boundary resistances in inhomogeneous quantum spin chains

et al. 2019

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Transport phenomena are central to physics, and transport in the many-body and fully-quantum regime is attracting an increasing amount of attention. It has been recently revealed that some quantum spin chains support ballistic transport of excitations at all energies. However, when joining two semi-infinite ballistic parts, such as the XX and XXZ spin-1/2 models, our understanding suddenly becomes less established. Employing a matrix-product-state ansatz of the wavefunction, we study the relaxation dynamics in this latter case. Here we show that it takes place inside a light cone, within which two qualitatively different regions coexist: an inner one with a strong tendency towards thermalization, and an outer one supporting ballistic transport. We comment on the possibility that even at infinite time the system supports stationary currents and displays a non-zero Kapitza boundary resistance. Our study paves the way to the analysis of the interplay between transport, integrability, and local defects.In 1941, P. Kapitza reported on the first measurement of the temperature drop near the boundary between helium and a solid when heat flows across the boundary [1]. The phenomenon, unrelated to that of conventional contact resistances, is ascribed to the mismatch between the energy carriers of the two materials, and appears even if the interface is perfect at the atomic scale. In the years 1951-1956, Kalatchnikov first, and Mazo and Onsager later, independently developed the so-called acoustic mismatch model, that gives a mathematical formulation to such intuition [2,3]. The quantitative comparison between experimental data and theoretical predictions motivated extensive investigations even in other interfaces without helium, e.g., between two solids [2], where the phenomenon has been often recovered.Owing to the difficulty of performing numerical simulations in order to benchmark the theory, simpler treatable models have been considered. In particular, focusing on junctions of classical one-dimensional (1D) harmonic chains enabled to quantitatively investigate the phenomenon of thermal boundary resistances [4][5][6]. The effect has been widely reproduced, and comparisons with suitable adaptations of the theory have been presented. Yet, a numerical investigation of the phenomenon in the fully quantum case has not been performed so far [7].The recent advances in the analytical understanding of the non-equilibrium dynamics of quantum spin chains [8][9][10][11][12] stimulated the improvement of state-of-theart numerical simulations addressing the unitary timeevolution of strongly-correlated 1D quantum models [13- * alberto.biella@univ-paris-diderot.fr 15]. Groundbreaking cold-atom experiments have also investigated several aspects of the coherent dynamics of closed quantum many-body systems [16][17][18][19][20][21][22][23][24]. These research efforts allowed to faithfully address how the presence of impurities and inhomogeneities may affect the quantum transport phenomena, also far from the linearresponse regime [25][26][2...

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“…The TEBD algorithm works equally well for non-Hermitian Hamiltonians generating nonunitary propagation. Indeed, it is widely used to study the NESS of incoherently driven chains where the coupling to the reservoirs is localized to one [76][77][78][79][80][81][82][83][84][85] or two sites [86][87][88][89] at the boundaries. We have now introduced all the elements required to extend the capabilities of TEBD to simulate the open system governed by the Hamiltonian Eq.…”

Section: Nonequilibrium Steady-state Solvermentioning

confidence: 99%

Tensor-Network Method to Simulate Strongly Interacting Quantum Thermal Machines

et al. 2020

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We present a methodology to simulate the quantum thermodynamics of thermal machines which are built from an interacting working medium in contact with fermionic reservoirs at a fixed temperature and chemical potential. Our method works at a finite temperature, beyond linear response and weak systemreservoir coupling, and allows for nonquadratic interactions in the working medium. The method uses mesoscopic reservoirs, continuously damped toward thermal equilibrium, in order to represent continuum baths and a novel tensor-network algorithm to simulate the steady-state thermodynamics. Using the example of a quantum-dot heat engine, we demonstrate that our technique replicates the well-known Landauer-Büttiker theory for efficiency and power. We then go beyond the quadratic limit to demonstrate the capability of our method by simulating a three-site machine with nonquadratic interactions. Remarkably, we find that such interactions lead to power enhancement, without being detrimental to the efficiency. Furthermore, we demonstrate the capability of our method to tackle complex many-body systems by extracting the superdiffusive exponent for high-temperature transport in the isotropic Heisenberg model. Finally, we discuss transport in the gapless phase of the anisotropic Heisenberg model at a finite temperature and its connection to charge conjugation parity, going beyond the predictions of single-site boundary driving configurations.

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High-temperature coherent transport in the XXZ chain in the presence of an impurity

Cited by 64 publications

References 76 publications

Eigenstate thermalization and quantum chaos in the Holstein polaron model

Eigenstate thermalization and quantum chaos in the Holstein polaron model

Ballistic transport and boundary resistances in inhomogeneous quantum spin chains

Tensor-Network Method to Simulate Strongly Interacting Quantum Thermal Machines

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