Related papers: Topological order, emergent gauge fields, and Ferm…
It is now widely recognized that the toric code is a pure gauge-theory model governed by a projective Hamiltonian with topological orders. In this work, we extend the interplay between quantum information system and gauge-theory model from…
The Hubbard model is studied in which disorder is introduced by putting the on-site interaction to zero on a fraction f of (impurity) sites of a square lattice. Using Quantum Monte Carlo methods and Dynamical Mean Field theory we find that…
We reconsider the problem of electrically charged, massless fermions scattering off magnetic monopoles. The interpretation of the outgoing states has long been a puzzle as, in certain circumstances, they necessarily carry fractional quantum…
Although topological artificial systems, like acoustic/photonic crystals and cold atoms in optical lattices were initially motivated by simulating topological phases of electronic systems, they have their own unique features such as the…
Quantum paramagnets are strongly-correlated phases of matter where competing interactions frustrate magnetic order down to zero temperature. In certain cases, quantum fluctuations induce instead topological order, supporting, in particular,…
We extend the twisted gauge theory model of topological orders in three spatial dimensions to the case where the three spaces have two dimensional boundaries. We achieve this by systematically constructing the boundary Hamiltonians that are…
We introduce three numerical methods for characterizing the topological phases of three-dimensional multiband Hubbard models based on twisted boundary conditions, Wilson loops, as well as the local topological marker. We focus on the…
Evolution of the order parameter in condensed matter analogues of cosmological phase transitions is discussed. It is shown that the density of the frozen-out topological defects is set by the competition between the quench rate -- the rate…
We analyze interacting ultra-cold bosonic atoms in a one-dimensional (1D) super-lattice potential with alternating tunneling rates t_1 and t_2 and inversion symmetry, which is the bosonic analogue of the Su-Schrieffer-Heeger (SSH) model. A…
The recent discovery of heavy-fermion superconductor UTe$_2$ has broadened the possibility of realizing exotic time-reversal-symmetry-breaking superconductivity. However, a comprehensive understanding of the topological phases in the…
We introduce lattice gauge theories which describe three-dimensional, gapped quantum phases exhibiting the phenomenology of both conventional three-dimensional topological orders and fracton orders, starting from a finite group $G$, a…
We study the XY model on a spherical surface inspired by recently realized spherically confined atomic gases. Instead of a traditional latitude-longitude lattice, we introduce a much more homogeneous spherical lattice, the Fibonacci…
We describe topologically ordered and fracton ordered states on novel geometries which do not have an underlying manifold structure. Using tree graphs such as the $k$-coordinated Bethe lattice ${\cal B}(k)$ and a hypertree called the…
Higher-order topological phases feature topologically protected boundary states in lower dimensions. Specifically, the zero-dimensional corner states are protected by the $d$th-order topology of a $d$-dimension system. In this work, we…
Topological mosaic pattern (TMP) can be formed in two-dimensional (2D) moir\'e superlattices, a set of periodic and spatially separated domains with distinct topologies give rise to periodic edge states on the domain walls. In this study,…
In this paper, we present our studies of the phase diagram of the cuprate superconductors performed in recent years. We describe how a few field-theoretical concepts can be used to account for the puzzling properties of these compounds.…
Topological photonics was embarked from realizing the first-order chiral state in gyromagnetic media, but its higher-order states were mostly studied in dielectric lattice instead. In this paper we theoretically unveil a hierarchy of…
In this paper, we apply the method of Fourier transform and basis rewriting developed in arXiv:1910.13441 for the two-dimensional quantum double model of topological orders to the three-dimensional gauge theory model (with a gauge group…
We introduce the theoretical framework we use to study the bewildering variety of phases in condensed--matter physics. We emphasize the importance of the breaking of symmetries, and develop the idea of an order parameter through several…
Possible ordered states in the 2D extended Hubbard model with on-site (U>0) and nearest-neighbor (V) interaction are examined near half filling, with emphasis on the effect of finite V. First, the phase diagram at absolute zero is…