arXiv subjects

D. Szász-Schagrin

Publications and source records attributed to D. Szász-Schagrin.

4 recordsLinked to original sources

arXiv2024

Relaxation dynamics in the (double) sine-Gordon model: An open-system viewpoint

We study the effects of integrability breaking on the relaxation dynamics of the (double) sine-Gordon model. Compared to previous studies, we apply an alternative viewpoint motivated by open-system physics by separating the phase field into homogeneous and inhomogeneous parts, describing a quantum pendulum (subsystem) and an interacting phononic bath (environment). To study the relaxation dynamics in the model, we perform quantum quenches using the mini-superspace-based truncated Hamiltonian approach developed recently and simulate the real-time evolution of various entanglement measures and the energy transfer between the subsystem and its environment. Our findings demonstrate that in the presence of integrability-breaking perturbations, the relaxation dynamics is substantially faster, signalled by the increase of entanglement and energy transfer between the quantum pendulum and the phonon bath.

cond-mat.stat-mech↗

arXiv2024

Sine-Gordon model at finite temperature: the method of random surfaces

We study the sine-Gordon quantum field theory at finite temperature by generalizing the method of random surfaces to compute the free energy and one-point functions of exponential operators non-perturbatively. Focusing on the gapped phase of the sine-Gordon model, we demonstrate the method's accuracy by comparing our results to the predictions of other methods and to exact results in the thermodynamic limit. We find excellent agreement between the method of random surfaces and other approaches when the temperature is not too small with respect to the mass gap. Extending the method to more general problems in strongly interacting one-dimensional quantum systems is discussed.

cond-mat.stat-mech↗

arXiv2023

Weak integrability breaking and level spacing distribution

Recently it was suggested that certain perturbations of integrable spin chains lead to a weak breaking of integrability in the sense that integrability is preserved at the first order in the coupling. Here we examine this claim using level spacing distribution. We find that the volume dependent crossover between integrable and chaotic level spacing statistics which marks the onset of quantum chaotic behaviour, is markedly different for weak vs. strong breaking of integrability. In particular, for the gapless case we find that the crossover coupling as a function of the volume $L$ scales with a $1/L^2$ law for weak breaking as opposed to the $1/L^3$ law previously found for the strong case.

cond-mat.stat-mech↗

arXiv2021

Quantum quenches in an interacting field theory: full quantum evolution vs. semi-classical approximations

We develop a truncated Hamiltonian method to investigate the dynamics of the $(1+1)d~ϕ^4$ theory following quantum quenches. The results are compared to two different semi-classical approaches, the self-consistent Gaussian approximation and the truncated Wigner approximation, and used to determine the range of validity of these widely used approaches. We show that the self-consistent approximation is strongly limited in comparison to the truncated Hamiltonian method which for larger cutoffs is practically exact for the parameter range studied. We find that the self-consistent approximation is only valid when the effective mass is in the vicinity of the renormalised mass. Similarly to the self-consistent approximation, the truncated Wigner approximation is not able to capture the correct mass renormalisation, and breaks down for strong enough interactions where the bare mass becomes negative. We attribute the failure of TWA to the presence of a classical symmetry broken fixed point. Besides establishing the truncated Hamiltonian approach as a powerful tool for studying the dynamics of the $ϕ^4$ model, our results on the limitation of semi-classical approximations are expected to be relevant for modelling the dynamics of other quantum field theories.

cond-mat.stat-mech↗