Hierarchy of the low-lying excitations for the $(2+1)$-dimensional $q=3$ Potts model in the ordered phase

Phase diagram of the three states Potts model with next nearest neighbor interactions on the Bethe lattice

We have found an exact phase diagram of the Potts model with next nearest neighbor interactions on the Bethe lattice of order two. The diagram consists of five phases: ferromagnetic, paramagnetic, modulated, antiphase and paramodulated, all meeting at the Lifshitz point i.e. $p=1/3$. We report on a new phase which we denote as paramodulated, found at low temperatures and characterized by 2-periodic points of an one dimensional dynamical system lying inside the modulated phase. Such a phase, inherent in the Potts model has no analogues in the Ising setting.

Critical properties of quantum three- and four-state Potts models with boundaries polarized along the transverse field

By computing the low-lying energy excitation spectra with the density matrix renormalization group algorithm we show that boundaries polarized in the direction of the transverse field lead to scale-invariant conformal towers of states at the critical point of the quantum four-state Potts model - a special symmetric case of the Ashkin-Teller model. Furthermore, by direct comparison of the excitation spectra we phenomenologically establish the duality between the transverse-polarized and three-state-mixed boundary conditions at the four-state Potts critical point. Finally, for completeness, we v…

From String Nets to Nonabelions

We discuss Hilbert spaces spanned by the set of string nets, i.e. trivalent graphs, on a lattice. We suggest some routes by which such a Hilbert space could be the low-energy subspace of a model of quantum spins on a lattice with short-ranged interactions. We then explain conditions which a Hamiltonian acting on this string net Hilbert space must satisfy in order for its ground state and low-lying quasiparticle excitations to be in the DFib topological phase. Using the string net wavefunction, we describe the properties of this phase. Our discussion is informed by mappings of string net wavefu…

广义吉布斯系综的模性质：形变KdV层级

Modular Properties of Generalised Gibbs Ensembles: The Deformed KdV Hierarchy

本文构造了量子KdV荷的形变守恒荷，定义相关递推与流方程并证明其性质，在c=1/2自由费米子理论和Lee-Yang模型中验证了其本征值与热力学Bethe Ansatz的一致性。

Entanglement Entropy and Entanglement Spectrum for Two-Dimensional Classical Spin Configuration

In quantum spin chains at criticality, two types of scaling for the entanglement entropy exist: one comes from conformal field theory (CFT), and the other is for entanglement support of matrix product state (MPS) approximation. They indicates that the matrix dimension of the MPS represents a length scale of spin correlation. On the other hand, the quantum spin-chain models can be mapped onto two-dimensional (2D) classical ones. Motivated by the scaling and the mapping, we introduce new entanglement entropy for 2D classical spin configuration as well as entanglement spectrum, and examine their …

重探Santa Fe模型的平均场理论：从零智能限价订单簿模型的精确BBGKY层级出发的系统推导

Mean-field theory of the Santa Fe model revisited: a systematic derivation from an exact BBGKY hierarchy for the zero-intelligence limit-order book model

本研究从动理学理论视角重探Santa Fe模型的平均场理论，通过精确主方程系统推导BBGKY层级方程，得到平均场解的显式闭合式，验证了相关近似的适用范围并修正了过往研究中的标度律错误。