arXiv subjects

Christian Eidecker-Dunkel

Publications and source records attributed to Christian Eidecker-Dunkel.

5 recordsLinked to original sources

arXiv2026

Absence of thermalization after a local quench and strong violation of the eigenstate thermalization hypothesis

Absence of thermalization after a global quantum quench is a well-established numerical observation in integrable many-body systems, and can be empirically related to a violation of the eigenstate thermalization hypothesis (ETH) in such models. Still, in many of those examples a weaker version of the conventional ETH (wETH) has been numerically reported or even rigorously proven. In this paper we show analytically and illustrate numerically that the absence of thermalization is already possible after a local quench. A closely related finding is a strong violation of the ETH, meaning that not even the wETH is fulfilled anymore. In our analytical explorations we focus on XX-spin-chain models with open boundary conditions, where the local quench is generated by initiating the system in thermal equilibrium and then suddenly switching on (or slightly changing) a single-spin impurity either at the end or in the center of the chain. Numerically we observe qualitatively similar phenomena also for more general XXZ-models in the case of an end-impurity, but not in the case of a central impurity.

cond-mat.stat-mech↗

arXiv2026

Basis dependence of eigenstate thermalization

Eigenstate thermalization refers to the property that an energy eigenstate of a many-body system is indistinguishable from a thermal equilibrium ensemble at the same energy as far as expectation values of local observables are concerned. In systems with degeneracies, the choice of an energy eigenbasis is not unique and the fraction of basis states exhibiting eigenstate thermalization can vary. We present a simple example where this fraction vanishes in the thermodynamic limit for one basis choice, but remains nonzero for another choice. In other words, the weak eigenstate thermalization hypothesis is satisfied in the first, but violated in the second basis. We furthermore prove that degeneracies must abound whenever a system is simultaneously symmetric under spatial translations and reflection. Finally, we derive general bounds on how strongly eigenstate thermalization may depend on the choice of the basis, and we reveal some interesting implications regarding the temporal relaxation properties of such systems.

cond-mat.stat-mech↗

arXiv2025

Thermalization in a simple spin-chain model

We consider the common spin-1/2 XX-model in one dimension with open boundary conditions and a large but finite number of spins. The system is in thermal equilibrium at times t<0, and is subject to a weak local perturbation (quantum quench) at t=0. Focusing mainly on single-spin perturbations and observables, we show that the system re-thermalizes for sufficiently large times t>0 without invoking any unproven assumptions besides the basic laws of quantum mechanics. Moreover, the time-dependent relaxation behavior is obtained in quantitative detail and is found to exhibit a wealth of interesting features.

cond-mat.stat-mech↗

arXiv2024

Onsager's regression hypothesis adjusted to quantum systems

Onsager's regression hypothesis connects the temporal relaxation of close-to-equilibrium systems with their dynamical correlation functions at thermal equilibrium. While the hypothesis is provably correct in classical systems, it is known to fail in the quantum regime. Here, we derive a suitably adjusted quantum version of Onsager's original hypothesis. Rigorous analytical results are complemented by a variety of numerical examples.

cond-mat.stat-mech↗

arXiv2023

Allosteric impurity effects in long spin chains

Allosterism traditionally refers to local changes in an extended object, for instance the binding of a ligand to a macromolecule, leading to a localized response at some other, possibly quite remote position. Here, we show that such fascinating effects may already occur in very simple and common quantum many-body systems, such as an anisotropic Heisenberg spin chain: Introducing an impurity at one end of a sufficiently long chain may lead to quite significant changes of the observable behavior near the other end, but not in the much larger region in between. Specifically, spin autocorrelation functions at thermal equilibrium are found to exhibit a pronounced allosterism of this type.

cond-mat.stat-mech↗