Characterizing correlations with full counting statistics: classical Ising and quantum XY spin chains

二维随机键伊辛模型低温相变与量子无限随机性

Low-temperature transition of 2d random-bond Ising model and quantum infinite randomness

研究二维随机键伊辛模型在低温下的相变行为，通过重整化群方法揭示其与量子无限随机性的关联，发现隧道指数与自旋刚性指数的关联。

Ising order parameter and topological phase transitions: Toric code in a uniform magnetic field

Quantum Ising model in a transverse field is of the simplest quantum many body systems used for studying universal properties of quantum phase transitions. Interestingly, it is well-known that such phase transitions can be mapped to topological phase transitions in Toric code models. Therefore, one can expect that well known properties of the transverse Ising model are used for characterizing topological phase transition in Toric code model. In this paper, we consider the magnetization of Ising model and show while it is a local order parameter, it is mapped to a non local order parameter in t…

Fermion loops and improved power-counting in two-dimensional critical metals with singular forward scattering

We analyze general properties of the perturbation expansion for two-dimensional quantum critical metals with singular forward scattering, such as metals at an Ising nematic quantum critical point and metals coupled to a U(1) gauge field. We derive asymptotic properties of fermion loops appearing as subdiagrams of the contributing Feynman diagrams -- for large and small momenta. Substantial cancellations are found in important scaling limits, which reduce the degree of divergence of Feynman diagrams with boson legs. Implementing these cancellations we obtain improved power-counting estimates th…

Quantum impurity spin in Majorana edge fermions

We show that Majorana edge modes of two-dimensional spin-triplet topological superconductors have Ising-like spin density whose direction is determined by the d-vector characterizing the spin-triplet pairing symmetry. Exchange coupling between an impurity spin (S=1/2) and Majorana edge modes is thus Ising-type. Under external magnetic field perpendicular to the Ising axis, the system can be mapped to a two-level system with Ohmic dissipation, which is equivalent to the anisotropic Kondo model. The magnetic response of the impurity spin can serve as a local experimental probe for the order para…

通过涂抹边界共形场论刻画能隙相：自发破缺广义对称性的非常规序中的对偶性

Characterizing gapped phases by smeared boundary conformal field theories: Duality in unusual ordering with spontaneously broken generalized symmetries

本文通过结合Higgs/Nambu-Goldstone型论证与涂抹边界共形场论，研究质量间隙相的对偶分类，揭示了质量间隙相可能超出边界临界现象范畴，并自发破缺非群状（不可逆）对称性。

Characterizing eigenstate thermalization via measures in the Fock space of operators

The eigenstate thermalization hypothesis (ETH) attempts to bridge the gap between quantum mechanical and statistical mechanical descriptions of isolated quantum systems. Here, we define unbiased measures for how well the ETH works in various regimes, by mapping general interacting quantum systems on regular lattices onto a single particle living on a high-dimensional graph. By numerically analyzing deviations from ETH behavior in the non-integrable Ising model, we propose a quantity that we call the $n$-$weight$ to democratically characterize the average deviations for all operators residing o…

由带拓扑约束的阻挫约瑟夫森结阵列涌现的长程伊辛自旋模型

Long-range Ising spins models emerging from frustrated Josephson junctions arrays with topological constraints

本研究理论分析带拓扑约束的阻挫约瑟夫森结Kagome晶格，推导长程各向异性伊辛自旋哈密顿量，揭示经典与量子区域的物相特征。

相互作用局域拓扑标记：一种用于表征相互作用和无序态拓扑的单粒子密度矩阵方法

Interacting Local Topological Markers: A one-particle density matrix approach for characterizing the topology of interacting and disordered states

本文提出基于单粒子密度矩阵的 Chern、chiral 和 Chern-Simons 局域拓扑标记，使其可在无需 Hamiltonian 的情况下表征相互作用与无序态拓扑。

One-step replica symmetry breaking solution for a highly asymmetric two-sublattice fermionic Ising spin glass model in a transverse field

The one-step replica symmetry breaking (RSB) is used to study a two-sublattice fermionic infinite-range Ising spin glass (SG) model in a transverse field $Γ$. The problem is formulated in a Grassmann path integral formalism within the static approximation. In this model, a parallel magnetic field $H$ breaks the symmetry of the sublattices. It destroys the antiferromagnetic (AF) order, but it can favor the nonergodic mixed phase (SG+AF) characterizing an asymmetric RSB region. In this region, intra-sublattice disordered interactions $V$ increase the difference between the RSB solutions of each …

Numerical study of a transition between Z2 topologically ordered phases

Distinguishing different topologically ordered phases and characterizing phase transitions between them is a difficult task due to the absence of local order parameters. In this paper, we use a combination of analytical and numerical approaches to distinguish two such phases and characterize a phase transition between them. The "toric code" and "double semion" models are simple lattice models exhibiting Z2 topological order. Although both models express the same topological ground state degeneracies and entanglement entropies, they are distinct phases of matter because their emergent quasi-par…

Extended Hubbard Model with Unconventional Pairing in Two Dimensions

We rigorously prove that an extended Hubbard model with attraction in two dimensions has an unconventional pairing ground state for any electron filling. The anisotropic spin-0 or anisotropic spin-1 pairing symmetry is realized, depending on a phase parameter characterizing the type of local attractive interactions. In both cases the ground state is unique. It is also shown that in a special case, where there are no electron hopping terms, the ground state has Ising-type Néel order at half-filling, when on-site repulsion is furthermore added. Physical applications are mentioned.