相关论文: Exploring Entropic Orders: High Temperature Contin…

Ordered phases of matter, such as solids, ferromagnets, superfluids, or quantum topological order, typically only exist at low temperatures. Despite this conventional wisdom, we present explicit local models in which all such phases persist…

Topological entanglement entropy is a topological invariant which can detect topological order of quantum many-body ground state. We assume an existence of such order parameter at finite temperature which is invariant under smooth…

We prove sufficient conditions for Topological Quantum Order at both zero and finite temperatures. The crux of the proof hinges on the existence of low-dimensional Gauge-Like Symmetries (that notably extend and differ from standard local…

Due to entropic effects, it is possible that generic high-energy states of a quantum or classical system are ordered. This leads to spontaneous symmetry breaking at arbitrarily high temperatures. We present minimal models of entropic order…

We identify a three-dimensional system that exhibits long-range entanglement at sufficiently small but nonzero temperature--it therefore constitutes a quantum topological order at finite temperature. The model of interest is known as the…

We introduce an exactly solvable lattice model that reveals a universal finite-size scaling law for configurational entropy driven purely by geometry. Using exact enumeration via Burnside's lemma, we compute the entropy for diverse 1D, 2D,…

We study topological order in a toric code in three spatial dimensions, or a 3+1D Z_2 gauge theory, at finite temperature. We compute exactly the topological entropy of the system, and show that it drops, for any infinitesimal temperature,…

Many-body quantum systems with local interactions undergo ``sudden death of entanglement" at high temperatures, whereby thermal states become classical mixtures of product states. We investigate whether symmetry constraints can prevent this…

We propose a diagnostic for finite temperature topological order using `topological entanglement negativity', the long-range component of a mixed-state entanglement measure. As a demonstration, we study the toric code model in $d$ spatial…

We analyze the free energy and construct the Gibbs-KMS states for a class of quantum lattice systems, at low temperatures and when the interactions are almost diagonal in a suitable basis. We study systems with continuous symmetry, but our…

Since the discovery of phase transitions driven by topological defects, the classification of phases of matter has been significantly extended beyond Ginzburg and Landau's paradigm of spontaneous symmetry breaking (SSB). In particular,…

Quantum many-body states that frequently appear in physics often obey an entropy scaling law, meaning that an entanglement entropy of a subsystem can be expressed as a sum of terms that scale linearly with its volume and area, plus a…

In this work the topological order at finite temperature in two-dimensional color code is studied. The topological entropy is used to measure the behavior of the topological order. Topological order in color code arises from the colored…

In this paper I intend to show that macroscopic entanglement is possible at high temperatures. I analyze multipartite entanglement produced by the $\eta$ pairing mechanism which features strongly in the fermionic lattice models of high…

Topologically ordered phases of matter elude Landau's symmetry-breaking theory, featuring a variety of intriguing properties such as long-range entanglement and intrinsic robustness against local perturbations. Their extension to…

Ordering at arbitrarily high temperature - entropic order - has been argued to take place in a class of generalized Ising models parameterised by a real interaction parameter $p$ when $p\ge 1$. We give a rigorous proof of this conjecture.…

We extend a recently defined measure of symmetry breaking, the entanglement asymmetry, to higher-form symmetries. In particular, we focus on Abelian topological order in two dimensions, which spontaneously breaks a 1-form symmetry. Using…

To explore the non-Euclidean generalization of higher-order topological phenomena, we construct a higher-order topological insulator model in hyperbolic lattices by breaking the time-reversal symmetry (TRS) of quantum spin Hall insulators.…

We compute the topological entropy of the toric code models in arbitrary dimension at finite temperature. We find that the critical temperatures for the existence of full quantum (classical) topological entropy correspond to the…

Recent work has shown that the entanglement of finite-temperature eigenstates in chaotic quantum many-body local Hamiltonians can be accurately described by an ensemble of random states with an internal $U(1)$ symmetry. We build upon this…