Quantum spin liquids are phases of matter whose internal structure is not captured by a local order parameter. Particularly intriguing are critical spin liquids, where strongly interacting excitations control low energy properties. Here we calculate their bipartite entanglement entropy that characterize their quantum structure. In particular we calculate the Renyi entropy $S_2$, on model wavefunctions obtained by Gutzwiller projection of a Fermi sea. Although the wavefunctions are not sign positive, $S_2$ can be calculated on relatively large systems (>324 spins), using the variational Monte Carlo technique. On the triangular lattice we find that entanglement entropy of the projected Fermi-sea state violates the boundary law, with $S_2$ enhanced by a logarithmic factor. This is an unusual result for a bosonic wave-function reflecting the presence of emergent fermions. These techniques can be extended to study a wide class of other phases.
Quantum spin liquids are highly fascinating quantum liquids in which the spin degrees of freedom fractionalize. An interesting class of spin liquids are the exactly solvable, three-dimensional Kitaev spin liquids. Their fractionalized excitations are Majonara fermions, which may exhibit a variety of topological band structures --- ranging from topologically protected Weyl semi-metals over nodal semi-metals to systems with Majorana Fermi surfaces. We study the entanglement spectrum of such Kitaev spin liquids and verify that it is closely related to the topologically protected edge spectrum. Mo…
In this paper, we study the entanglement entropy between two SYK systems with bilinear coupling. We use the replica trick to calculate the entanglement entropy in the ground state. In parallel, we calculate the entanglement entropy through the Ryu-Takayanagi formula in gravity. For the ground state that is dual to an eternal traversable wormhole in AdS_2, the bulk quantum correction to the entanglement entropy is of the same order as the minimal surface area. The ground state of the coupled system is close to a thermofield double state with particular temperature and they have the same entangl…
Entanglement Entropy of Coupled Conformal Field Theories and Fermi Liquids
本文计算了一般空间维d中两个耦合无隙系统的纠缠熵。无带隙系统可以是共形场论（CFT）或费米液体。我们假设两个系统在空间的h维子流形中一致耦合，其中0 <= h <= d。我们将着重讨论纠缠熵与系统大小的关系以及与系统间耦合常数g的关系。我们的计算采用三种方法：（1）基态波泛函的精确计算，（2）泛函路径积分的微扰计算，（3）标度变元。
We present a new method for calculating Renyi entanglement entropies for fermionic field-theories originating from microscopic Hamiltonians. The method builds on an operator identity which we discover for the first time. The identity leads to the representation of traces of operator products, and thus Renyi entropies of a subsystem, in terms of fermionic-displacement operators. This allows for a very transparent path-integral formulation, both in and out-of-equilibrium, having a simple boundary condition on the fermionic fields. The method is validated by reproducing well known expressions for…
Topological order, reflected in long range patterns of entanglement, is quantified by the topological entanglement entropy (TEE) $γ$. We show that for gapped quantum spin liquids (QSL) it is possible to extract $γ$ using two-spin local correlators. We demonstrate our method for the gapped $\mathbb{Z}_2$ Kitaev spin liquid on a honeycomb lattice with anisotropic interactions. We show that the $γ= \log 2$ for $\mathbb{Z}_2$ topological order can be simply extracted from local two-spin correlators across two different bonds, with an accuracy comparable or higher than the Kitaev-Preskill construct…
A useful way to obtain the central charge of entanglement Hamiltonian -- Nested entanglement entropy
在本文中，我们回顾了如何通过嵌套纠缠熵获得临界纠缠哈密顿量的中心荷，这是在[J. Lou et al. PRB 84，245128（2011）]中首次引入的。由嵌套纠缠熵得到的中心荷可以识别纠缠哈密顿量的临界现象。我们回顾了我们以前的研究[J. Lou等人PRB 84，245128（2011），S. Tanaka et al. PRA 87，214401（2013）]，其中我们使用嵌套纠缠熵研究了二维价键固体（VBS）态和正方形和三角形梯子上的量子硬正方形模型的某些纠缠性质。
Entanglement entropy in topologically ordered matter phases has been computed extensively using various methods. In this paper, we study the entanglement entropy of topological phases in two-spaces from a new perspective---the perspective of quasiparticle fluctuations. In this picture, the entanglement spectrum of a topologically ordered system is identified with the spectrum of quasiparticle fluctuations of the system, and the entanglement entropy measures the maximal quasiparticle fluctuations on the EB. As a consequence, entanglement entropy corresponds to the thermal entropy of the quasipa…
The Quantum Null Energy Condition (QNEC) relates energy to the second variation of entropy in relativistic quantum field theory. We use the QNEC inequality to bound entanglement entropy in quenches. At early times the entanglement entropy grows quadratically in time, and the QNEC provides an upper bound on the prefactor. We demonstrate that the bound is tight, by showing that it is saturated in certain quench protocols: boundary state quenches in conformal field theories in any dimensions. In higher than two dimensions we compute entanglement entropy using AdS/CFT. Our results are the first pu…
We study the ground-state entanglement of gapped domain walls between topologically ordered systems in two spatial dimensions. We derive a universal correction to the ground-state entanglement entropy, which is equal to the logarithm of the total quantum dimension of a set of superselection sectors localized on the domain wall. This expression is derived from the recently proposed entanglement bootstrap method.
