Nonthermal States Arising from Confinement in One and Two Dimensions

Abstract

We show that confinement in the quantum Ising model leads to nonthermal eigenstates, in both continuum and lattice theories, in both one (1D) and two dimensions (2D). In the ordered phase, the presence of a confining longitudinal field leads to a profound restructuring of the excitation spectrum, with the low-energy two-particle continuum being replaced by discrete 'meson' modes (linearly confined pairs of domain walls). These modes exist far into the spectrum and are atypical, in the sense that expectation values in the state with energy E do not agree with the microcanonical (thermal) ensemble prediction. Single meson states persist above the two meson threshold, due to a surprising lack of hybridization with the (n ≥ 4)-domain wall continuum, a result that survives into the thermodynamic limit and that can be understood from analytical calculations. The presence of such states is revealed in anomalous post-quench dynamics, such as the lack of a light cone, the suppression of the growth of entanglement entropy, and the absence of thermalization for some initial states. The nonthermal states are confined to the ordered phase -the disordered (paramagnetic) phase exhibits typical thermalization patterns in both 1D and 2D in the absence of integrability.

Quantum information scrambling after a quantum quench

“…Concomitantly, further checks of the d −2/3 decay in other non-interacting systems are necessary to assess its universality. A natural question is also whether a crossover between algebraic and exponential decay can take place in models with unstable but long lived quasiparticles, as for instance in prethernalization scenario [85][86][87][88] or in confining models [89][90][91][92][93]. Finally, it would be interesting to investigate the mutual information scrambling in those models without a maximum quasiparticle velocity, such as integrable non-relativistic quantum field theories.…”

Quantum scars as embeddings of weakly broken Lie algebra representations

“…1, 28,29 Such atypical eigenstates have previously been rigorously constructed in the non-integrable Affleck-Kennedy-Lieb-Tasaki (AKLT) model. 30,31 While the collection of models that feature scarred-like eigenstates has recently expanded, [32][33][34][35][36][37][38][39][40][41][42][43] a smaller subset of such models have been demonstrated to display revivals from easily preparable initial states. [44][45][46] Thus, the connection between revivals and the presence of atypical eigenstates remains to be fully understood.…”

Systematic Construction of Scarred Many-Body Dynamics in 1D Lattice Models

“…In a related development, it was proposed that atypical eigenstates of one Hamiltonian can be "embedded" into the spectrum of another, ETH-violating, Hamiltonian [33]. However, although the collection of models that feature atypical eigenstates is rapidly expanding [34][35][36][37][38], including recent examples of topological phases [39] and fractons [40], their relation to periodic dynamics remains largely unclear.In this paper we systematically construct interacting lattice models that exhibit periodic quantum revivals when quenched from a particular product state. The basic building block has a Hilbert space containing N c states ("colors") and a time-independent Hamiltonian that yields periodic unitary dynamics, U(t + T ) = U(t).…”