Entanglement Hamiltonian during a domain wall melting in the free Fermi chain

Abstract

We study the unitary time evolution of the entanglement Hamiltonian of a free Fermi lattice gas in one dimension initially prepared in a domain wall configuration. To this aim, we exploit the recent development of quantum fluctuating hydrodynamics. Our findings for the entanglement Hamiltonian are based on the effective field theory description of the domain wall melting and are expected to exactly describe the Euler scaling limit of the lattice gas. However, such field theoretical results can be recovered from high-precision numerical lattice calculations only when summing appropriately over all the hoppings up to distant sites.

Local and non-local properties of the entanglement Hamiltonian for two disjoint intervals

“…Interchanging j → −j, one clearly arrives at the same definition of the weights as in (29) for the double interval. Hence, in the limit N → ∞, one has S(x i ) → 2π β (x) as well as C(x i ) → 0, perfectly reproducing the result (37) and (38) for the boundary Dirac theory with α = 0, π. The case 0 < α < π can also be studied on the lattice by introducing a chemical potential at the first site, i.e.…”

“…For slowly varying inhomogeneities, the continuum entanglement Hamiltonian for a single interval can be obtained [36] via the curved-space CFT approach [37]. Recently it has been shown that the continuum limit can be generalized to recover the local terms for the domainwall melting problem [38]. It would be interesting to check whether this treatment could be extended to the bi-local terms in case of two intervals.…”

“…The result (45) already makes it clear that the relation between the half-chain problem and the double interval is completely analogous to the continuum case in section 5.1. However, it remains to understand the difference between the bi-local operators (38) and (7), by considering the continuum limit of H ± . We first apply the substitutions (21), where the left/right-moving fields are coupled via the boundary condition (36) at x = 0.…”

Electrostatic solution of massless quenches in Luttinger liquids

“…More recently, various inhomogeneous generalisations of (1) were studied in connection to inhomogeneous and time-dependent problems in TLLs, both in- [7][8][9][10][11][12][13] and out-of-equilibrium [8,[14][15][16][17][18][19][20][21][22][23][24], mainly aiming at describing gases in traps and their non-equilibrium dynamics (see Section V in Ref. [25] for a more comprehensive review of the literature).…”

Domain wall melting across a defect

“…In this manuscript, we prepare an initial state with a domain wall localised at the defect and we let it melt. Without the defect, this is a protocol that has been studied intensively in the free fermionic literature [32][33][34][35][36][37][38][39][40][41][42][43][44][45] and it represents a case study for the application of hydrodynamics to non-equilibrium quantum systems (recently adapted also to interacting integrable models [46,47] with the generalised hydrodynamics formalism [48,49]). Anyhow, the presence of the defect is expected to alter dramatically the evolution at a qualitative level.…”