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arXiv:1406.0648 · Physica Scripta

Work statistics, irreversible heat and correlations build-up in joining two spin chains

Tony J. G. Apollaro, Gianluca Francica, Mauro Paternostro, Michele Campisi

Published Oct 1, 2015• 22 citations
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Abstract

We investigate the influences of quantum many-body effects, such as criticality and the existence of factorization fields, in the thermodynamic cost of establishing a bonding link between two independent quantum spin chains. We provide a physical interpretation of the behavior of irreversible work spent in such a process by linking the phenomenology of such quantities to the properties of the spectrum of the system.

DOI
10.1088/0031-8949/2015/t165/014023

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We investigate the influences of quantum many-body effects, such as criticality and the existence of factorization fields, in the thermodynamic cost of establishing a bonding link between two independent quantum spin chains. We provide a physical interpretation of the behavior of irreversible work spent in such a process by linking the phenomenology of such quantities to the properties of the spectrum of the system.
Thermodynamic properties of the quantum Heisenberg spin chains with S=1/2,S=1/2,S=1/2, 1, and 3/23/23/2 are investigated using the transfer-matrix renormalization-group method. The temperature dependence of the magnetization, susceptibility, specific heat, spin-spin correlation length, and several other physical quantities in a zero or finite applied field are calculated and compared. Our data agree well with the Bethe ansatz, exact diagonalization, and quantum Monte Carlo results and provide further insight into the quantum effects in the antiferromagnetic Heisenberg spin chains.
The thermodynamic behavior of out-of-equilibrium quantum systems in finite-time dynamics encompasses the description of energy fluctuations, which dictates a series of the system's physical properties. In addition, strong interactions in many-body systems strikingly affect the energy-fluctuation statistics along a nonequilibrium dynamics. By driving transient currents to oppose the precursor to the metal-Mott-insulator transition in a diversity of dynamical regimes, we show how increasing many-body interactions dramatically affect the statistics of energy fluctuations and, consequently, the extractable work distribution of finite Hubbard chains. Statistical properties of such distributions as its skewness with its impressive change across the transition can be related to irreversibility and entropy production. Even for slow driving rates, the quasi quantum phase transition hinders equilibration, increasing the process irreversibility, and inducing strong features in the work distribution. In the Mott-insulating phase, the work fluctuation-dissipation balance gets modified with the irreversible entropy production dominating over work fluctuations. Because of this, effects of an interaction-driven quantum phase transition on thermodynamic quantities and irreversibility must be considered in the design of protocols in small-scale devices for application in quantum technology. Eventually, such many-body effects can also be employed in work extraction and refrigeration protocols on a quantum scale.
The statistics of the heat exchanged between two quantum XX spin chains prepared at different temperatures is studied within the assumption of weak coupling. This provides simple formulas for the average heat and its corresponding characteristic function, from which the probability distribution may be computed numerically. These formulas are valid for arbitrary sizes and therefore allow us to analyze the role of the thermodynamic limit in this nonequilibrium setting. It is found that all thermodynamic quantities are extremely sensitive to the quantum phase transition of the XX chain.
We consider thermodynamic properties, e.g. specific heat and magnetic susceptibility, of alternating Heisenberg spin chains. Due to a hidden Ising symmetry, these chains can be decomposed into a set of finite chain fragments. The problem of finding the thermodynamic quantities is effectively separated into two parts. First we deal with finite objects; secondly we can incorporate the fragments into a statistical ensemble. As functions of the coupling constants, the models exhibit special features in the thermodynamic quantities, e.g. the specific heat displays double peaks at low enough temperatures. These features stem from first-order quantum phase transitions at zero temperature, which have been investigated in the first part of this work.
Abstract The thermodynamic implications for the out-of-equilibrium dynamics of quantum systems are to date largely unexplored, especially for quantum many-body systems. In this paper we investigate the paradigmatic case of an array of nearest-neighbor coupled quantum harmonic oscillators interacting with a thermal bath and subjected to a quench of the inter-oscillator coupling strength. We study the work done on the system and its irreversible counterpart, and characterize analytically the fluctuation relations of the ensuing out-of-equilibrium dynamics. Finally, we showcase an interesting functional link between the dissipated work produced across a two-element chain and their degree of general quantum correlations. Our results suggest that, for the specific model at hand, the non-classical features of a harmonic system can influence significantly its thermodynamics.
The emerging field of quantum thermodynamics is contributing important results and insights into archetypal many-body problems, including quantum phase transitions. Still, the question whether out-of-equilibrium quantities, such as fluctuations of work, exhibit critical scaling after a sudden quench in a closed system has remained elusive. Here, we take a novel approach to the problem by studying a quench across an impurity quantum critical point. By performing density matrix renormalization group computations on the two-impurity Kondo model, we are able to establish that the irreversible work produced in a quench exhibits finite-size scaling at quantum criticality. This scaling faithfully predicts the equilibrium critical exponents for the crossover length and the order parameter of the model, and, moreover, implies an exponent for the rescaled irreversible work. By connecting the irreversible work to the two-impurity spin correlation function, our findings can be tested experimentally.