Quantum quenches and thermalization in one-dimensional fermionic systems

By Marcos Rigol. 2009

173 citations recorded by the source corpus.

We study the dynamics and thermalization of strongly correlated fermions in finite one-dimensional lattices after a quantum quench. Our calculations are performed using exact diagonalization. We focus on one- and two-body observables such as the momentum distribution function $[n(k)]$ and the density-density structure factor $[N(k)]$, respectively, and study the effects of approaching an integrable point. We show that while the relaxation dynamics and thermalization of $N(k)$ for fermions is very similar to the one of hardcore bosons, the behavior of $n(k)$ is distinctively different. The latter observable exhibits a slower relaxation dynamics in fermionic systems. We identify the origin of this behavior, which is related to the off-diagonal matrix elements of $n(k)$ in the basis of the eigenstates of the Hamiltonian. More generally, we find that thermalization occurs far away from integrability and that it breaks down as one approaches the integrable point.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d4e877b43df598f33057f74b597bc3b139f52d58

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

One dimensional bosons: From condensed matter systems to ultracold gases (2011, background): “However, thermalization and the eigenstate thermalization hypothesis break down as one approaches an integrable point (Rigol, 2009a,b; Roux, 2010).”
Thermalization near Integrability in a Dipolar Quantum Newton's Cradle (2017, background): “Moreover, numerical exploration of such questions is challenging because the achievable system sizes are quite small if one wishes to simulate to arbitrarily long times [11, 12].”
Nonequilibrium dynamical mean-field theory and its applications (2013, background): “On the other hand, even small integrability-breaking terms inthe Hamiltonian can lead to thermalization after sufficiently long times (Rigol, 2009a,b). b. Interaction quench in the Falicov-Kimball model and the role of conserved quantities For an interaction quench in the FalicovKimball (FK) model…”
Generalized Gibbs ensemble in integrable lattice models (2016, background): “12 and 13 is very similar to the one seen for various observables in nonintegrable one-dimensional systems, which exhibit eigenstate thermalization [86, 87].”