Related papers: Automorphic equivalence within gapped phases in th…
We expand upon the standard quantum adiabatic theorem, examining the time-dependence of quantum evolution in the near-adiabatic limit. We examine a Hamiltonian that evolves along some fixed trajectory from $\hat{H}_0$ to $\hat{H}_1$ in a…
A set of new exact ground states of the generalized Hubbard models in arbitrary dimensions with explicitly given parameter regions is presented. This is based on a simple method for constructing exact ground states for homogeneous quantum…
Traditional quantum physics solves ground states for a given Hamiltonian, while quantum information science asks for the existence and construction of certain Hamiltonians for given ground states. In practical situations, one would be…
In order to describe unbalanced ultracold fermionic quantum gases on optical lattices in a harmonic trap, we investigate an attractive ($U<0$) asymmetric ($t_\uparrow\neq t_\downarrow$) Hubbard model with a Zeeman-like magnetic field. In…
We consider the problem of the explicit description of the gauge-invariant subspace of pure lattice gauge theories in the Hamiltonian formulation, where the gauge group is either a compact Lie group or a finite group. The latter case is…
The first proof of the quantum adiabatic theorem was given as early as 1928. Today, this theorem is increasingly applied in a many-body context, e.g. in quantum annealing and in studies of topological properties of matter. In this setup,…
We propose an operator generalization of the Li-Haldane conjecture regarding the entanglement Hamiltonian of a disk in a 2+1D chiral gapped groundstate. The logic applies to regions with sharp corners, from which we derive several universal…
We investigate the persistence of spectral gaps of one-dimensional frustration free quantum lattice systems under weak perturbations and with open boundary conditions. Assuming the interactions of the system satisfy a form of local…
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 present straightforward proofs of estimates used in the adiabatic approximation. The gap dependence is analyzed explicitly. We apply the result to interpolating Hamiltonians of interest in quantum computing.
Adiabatic time evolution of quantum systems is a widely used tool with applications ranging from state preparation through simplifications of computations and topological transformations to optimization and quantum computing. Adiabatic time…
For multi-level time-dependent quantum systems one can construct superadiabatic representations in which the coupling between separated levels is exponentially small in the adiabatic limit. Based on results from [BeTe1] for special…
We investigate the connection between local minima in the problem Hamiltonian and first order quantum phase transitions during an adiabatic quantum computation. We demonstrate how some properties of the local minima can lead to an extremely…
There is a renewed interest in the uncertainty principle, reformulated from the information theoretic point of view, called the entropic uncertainty relations. They have been studied for various integrable systems as a function of their…
We adapt the Goldstone theorem to study spontaneous symmetry breaking in relativistic theo- ries at finite charge density. It is customary to treat systems at finite density via non-relativistic Hamiltonians. Here we highlight the…
In [Can et al. 2016], quantum Hall states on singular surfaces were shown to possess an emergent conformal symmetry. In this paper, we develop this idea further and flesh out details on the emergent conformal symmetry in holomorphic…
We provide a method for estimating spectral gaps in low-dimensional systems. Unlike traditional phase estimation, our approach does not require ancillary qubits nor does it require well characterised gates. Instead, it only requires the…
We study effectively one-dimensional systems that emerge at the edge of a two-dimensional topologically ordered state, or at the boundary between two topologically ordered states. We argue that anyons of the bulk are associated with…
The adiabatic theorem in quantum mechanics implies that if a system is in a discrete eigenstate of a Hamiltonian and the Hamiltonian evolves in time arbitrarily slowly, the system will remain in the corresponding eigenstate of the evolved…
We give a quantum algorithm for solving instances of the satisfiability problem, based on adiabatic evolution. The evolution of the quantum state is governed by a time-dependent Hamiltonian that interpolates between an initial Hamiltonian,…