Related papers: The complete set of infinite volume ground states …
Transitions between different topologically ordered phases have been studied by artificially creating boundaries between these gapped phases and thus studying their effects relating to condensation and tunneling of particles from one phase…
We consider general classes of gradient models on regular trees with values in a countable Abelian group $S$ such as $\mathbb{Z}$ or $\mathbb{Z}_q$, in regimes of strong coupling (or low temperature). This includes unbounded spin models…
We study the Twisted Kitaev Quantum Double model within the framework of Local Topological Order (LTO). We extend its definition to arbitrary 2D lattices, enabling an explicit characterization of the ground state space through the invariant…
We show that in presence of an applied external field the two-component order parameter superconductor falls in two categories of ground states, namely, in the traditional Abrikosov ground state or in a new ground state fitted to describe a…
We introduce a broad class of simple models for quantum Hall states based on the expansion of their parent Hamiltonians near the one-dimensional limit of "thin cylinders", i.e. when one dimension $L_y$ of the Hall surface becomes comparable…
We consider a gas of $N$ bosons in a box with volume one interacting through a two-body potential with scattering length of order $N^{-1}$ (Gross-Pitaevskii limit). Assuming the (unscaled) potential to be sufficiently small, we show that…
We address a number of conjectures about the ground state O(1) loop model, computing in particular two infinite series of partial sums of its entries and relating them to the enumeration of plane partitions. Our main tool is the use of…
Solving for quantum ground states is important for understanding the properties of quantum many-body systems, and quantum computers are potentially well-suited for solving for quantum ground states. Recent work has presented a nearly…
Kitaev's quantum double model is a lattice gauge theoretic realization of Dijkgraaf-Witten topological quantum field theory (TQFT), its topologically protected ground state space has broad applications for topological quantum computation…
We compare and contrast the entanglement in the ground state of two Jahn-Teller models. The $E\otimes\beta$ system models the coupling of a two-level electronic system, or qubit, to a single oscillator mode, while the $E\otimes\epsilon$…
We consider the k-folded sine-Gordon model, obtained from the usual version by identifying the scalar field after k periods of the cosine potential. We examine (1) the ground state energy split, (2) the lowest lying multi-particle state…
Recently there has been a great interest in understanding quantum spin liquid phases with varying spin magnitude, partly due to possible material realizations. A number of recent numerical computations suggest that the ground state of the…
Motivated by the $\Omega$-spectrum proposal of unique gapped ground states by Kitaev, we study adiabatic cycles in gapped quantum spin systems from various perspectives. We give a few exactly solvable models in one and two spatial…
Kitaev's quantum double models, including the toric code, are canonical examples of quantum topological models on a 2D spin lattice. Their Hamiltonian defines the groundspace by imposing an energy penalty to any nontrivial flux or charge,…
In this paper, we systematically review mathematical models, theories and numerical methods for ground states and dynamics of spinor Bose-Einstein condensates (BECs) based on the coupled Gross-Pitaevskii equations (GPEs). We start with a…
Inspired by the Affleck-Kennedy-Lieb-Tasaki (AKLT) model, we present exact solutions for a spin-1 chain with Kitaev-like couplings. We consider an expanded Kitaev model with bilinear and biquadratic terms. At an exactly solvable point, the…
The macroscopic theory of anyon condensation, rooted in the categorical structure of topological excitations, provides a complete classification of gapped boundaries in topologically ordered systems, where distinct boundaries correspond to…
We study in this paper the ground state energy of a free bosonic theory on a finite interval of length $R$ with either a pair of sine-Gordon type or a pair of Kondo type interactions at each boundary. This problem has potential applications…
We consider a general one-dimensional tight-binding electron model which has a period $P$. For any filling factor $\nu$ such that $P\nu$ is non-integral, we prove that the model in the infinite volume limit has either a symmetry breaking or…
We find all the exact eigenstates and eigenvalues of a spin-1/2 model on square lattice: $H=16g \sum_i S^y_i S^x_{i+x} S^y_{i+x+y} S^x_{i+y}$. We show that the ground states for $g<0$ and $g>0$ have different quantum orders described by Z2A…