Entanglement and classical fluctuations at finite-temperature critical points

Abstract

We investigate several entanglement-related quantities at finite-temperature criticality in the three-dimensional quantum spherical model, both as a function of temperature T and of the quantum parameter g, which measures the strength of quantum fluctuations. While the von Neumann and the Rényi entropies exhibit the volume-law for any g and T , the mutual information obeys an area law. The prefactors of the volume-law and of the area-law are regular across the transition, reflecting that universal singular terms vanish at the transition. This implies that the mutual information is dominated by nonuniversal contributions. This hampers its use as a witness of criticality, at least in the spherical model. We also study the logarithmic negativity. For any value of g, T , the negativity exhibits an area-law. The negativity vanishes deep in the paramagnetic phase, it is larger at small temperature, and it decreases upon increasing the temperature. For any g, it exhibits the so-called sudden death, i.e., it is exactly zero for large enough T . The vanishing of the negativity defines a "death line", which we characterise analytically at small g. Importantly, for any finite T the area-law prefactor is regular across the transition, whereas it develops a cusp-like singularity in the limit T → 0. Finally, we consider the single-particle entanglement and negativity spectra. The vast majority of the levels are regular across the transition. Only the larger ones exhibit singularities. These are related to the presence of a zero mode, which reflects the symmetry breaking. This implies the presence of sub-leading singular terms in the entanglement entropies. Interestingly, since the larger levels do not contribute to the negativity, sub-leading singular corrections are expected to be suppressed for the negativity.

Symmetry resolved entanglement in gapped integrable systems: a corner transfer matrix approach

“…Our Eq. (74) paves the way for general numerical studies in arbitrary dimension for bosonic systems as well, also in the presence of a spherical constraint [76]. In some cases, also analytical results can be explicitly worked out [77].…”

Noninteracting fermionic systems with localized losses: Exact results in the hydrodynamic limit

“…An intriguing question is how local dissipation affects the entanglement scaling at finite-temperature critical points. An ideal setup to explore this is provided by the so-called quantum spherical model, for which entanglement properties can be studied effectively [78][79][80] . Furthermore, it would be of interest to study how localized gain/loss dissipations may affect entanglement spreading, for instance, by studying the dynamics of the logarithmic negativity [81][82][83][84] and comparing with the quasiparticle picture 85 .…”

Symmetry decomposition of negativity of massless free fermions

“…The moments R n with integer n ≥ 2 can also be measured in experiments [19][20][21], but they are not entanglement monotones. The entanglement negativity and Rényi negativities have been used to characterise mixed states in various quantum systems such as in harmonic oscillator chains [22][23][24][25][26][27][28][29][30], quantum spin models [31][32][33][34][35][36][37][38][39][40][41][42][43][44], (1+1)d conformal and integrable field theories [17,18,[45][46][47][48][49][50][51][52], topologically ordered phases of matter in (2+1)d [53][54][55][56][57], out-of-equilibrium settings [20,[58][59][60][61][62]…”