Related papers: Automorphic equivalence within gapped phases in th…
We prove an adiabatic theorem for general densities of observables that are sums of local terms in finite systems of interacting fermions, without periodicity assumptions on the Hamiltonian and with error estimates that are uniform in the…
We establish adiabatic theorems with and without spectral gap condition for general -- typically dissipative -- linear operators $A(t): D(A(t)) \subset X \to X$ with time-dependent domains $D(A(t))$ in some Banach space $X$. In these…
The low-temperature physics of quantum many-body systems is largely governed by the structure of their ground states. Minimizing the energy of local interactions, ground states often reflect strong properties of locality such as the area…
The affine coherent states quantization is a promising integral quantization of Hamiltonian systems when the phase space includes at least one conjugate pair of variables which takes values from a half-plane. Such a situation is common for…
We extend the single-particle topological classification of insulators and superconductors to include systems in which disorder preserves average reflection symmetry. We show that the topological group structure of bulk Hamiltonians and…
The existence of an excitation gap in the bulk spectrum is one of the most prominent fingerprints of topological phases of matter. In this paper, we propose a family of two dimensional Hamiltonians that yield an unusual class $D$…
By analyzing an exactly solvable model in the second quantized formulation which allows a unified treatment of adiabatic and non-adiabatic geometric phases, it is shown that the topology of the adiabatic Berry's phase, which is…
We consider the edge and bulk conductances for 2D quantum Hall systems in which the Fermi energy falls in a band where bulk states are localized. We show that the resulting quantities are equal, when appropriately defined. An appropriate…
It is shown that Berry's phase associated with the adiabatic change of local variables in the Hamiltonian can be used to characterize the multimode Peierls state, which has been proposed as a new type of the ground state of the…
In this article we formulate and prove sufficient conditions for the existence of trajectories of nonstationary periodic solutions of autonomous Hamiltonian systems in a neighbourhood of equilibria. It is worth pointing out that assumptions…
Spontaneous symmetry-breaking in phase transitions occurs when the system Hamiltonian is symmetric under a certain transformation, but the equilibrium states observed in nature are not. Here, we prove that when a discrete symmetry is…
It is well known that an exponentially localized Hamiltonian must be gapless if its ground state has algebraic correlations. We show that even certain exponentially decaying correlations can imply gaplessness. This is exemplified by the…
The gauge invariance of geometric phases for mixed states is analyzed by using the hidden local gauge symmetry which arises from the arbitrariness of the choice of the basis set defining the coordinates in the functional space. This…
We present generalized adiabatic theorems for closed and open quantum systems that can be applied to slow modulations of rapidly varying fields, such as oscillatory fields that occur in optical experiments and light induced processes. The…
Models of quantum computation are important because they change the physical requirements for achieving universal quantum computation (QC). For example, one-way QC requires the preparation of an entangled "cluster" state followed by…
Quantum entanglement marks a definitive feature of topological states. However, the entanglement spectrum remains insufficiently explored for topological states without a bulk energy gap. Using a combination of field theory and numerical…
The conventional formulation of the non-adiabatic (Aharonov-Anandan) phase is based on the equivalence class $\{e^{i\alpha(t)}\psi(t,\vec{x})\}$ which is not a symmetry of the Schr\"{o}dinger equation. This equivalence class when understood…
We study the question of what kind of a macroscopic superposition can(not) naturally exist as a ground state of some gapped local many-body Hamiltonian. We derive an upper bound on the energy gap of an arbitrary physical Hamiltonian…
Adiabatic state preparation provides an analytical solution for generating the ground state of a target Hamiltonian, starting from an easily prepared ground state of the initial Hamiltonian. While effective for time-dependent Hamiltonians…
In his famous 1981 talk, Feynman proposed that unlike classical computers, which would presumably experience an exponential slowdown when simulating quantum phenomena, a universal quantum simulator would not. An ideal quantum simulator…