Related papers: Classification of gapped ground state phases in qu…
In this short note, I review some recent results about gapped ground state phases of quantum spin systems and discuss the notion of topological order.
Quantum many-body systems divide into a variety of phases with very different physical properties. The question of what kind of phases exist and how to identify them seems hard especially for strongly interacting systems. Here we make an…
We discuss the role of compact symmetry groups, G, in the classification of gapped ground state phases of quantum spin systems. We consider two representations of G on infinite subsystems. First, in arbitrary dimensions, we show that the…
We consider the classification problem of symmetry protected topological (SPT) phases on quantum spin systems. SPT phases are gapped short-range-entangled quantum phases with a symmetry $G$. We explain that in one and two-dimensional…
I discuss the concept of quasi-state decompositions for ground states and equilibrium states of quantum spin systems. Some recent results on the ground states of a class of one-dimensional quantum spin models are summarized and new work in…
We study the classification problem of mixed states in two-dimensional quantum spin systems in the operator algebraic framework of quantum statistical mechanics. We associate a braided $C^*$-tensor category to each state satisfying a…
We introduce a class of gapped Hamiltonians on quantum spin chains, which allows asymmetric edge ground states. This class is an asymmetric generalization of the class of Hamiltonians in [FNS]. It can be characterized by five qualitative…
The ground states of an abstract model in quantum field theory are investigated. By means of the asymptotic field theory, we give a necessary and sufficient condition for that the expectation value of the number operator of ground states is…
Phase-space path-integrals are used in order to illustrate various aspects of a recently proposed interpretation of quantum mechanics as a gauge theory of metaplectic spinor fields.
We present a binary classifier based on neural networks to detect gapped quantum phases. By considering the errors on top of a suitable reference state describing the gapped phase, we show that a neural network trained on the errors can…
Quantum phases with different orders exist with or without breaking the symmetry of the system. Recently, a classification of gapped quantum phases which do not break time reversal, parity or on-site unitary symmetry has been given for 1D…
In this paper, we present a homotopical framework for studying invertible gapped phases of matter from the point of view of infinite spin lattice systems, using the framework of algebraic quantum mechanics. We define the notion of quantum…
We introduce a general analytic approach to the study of factorization points and factorized ground states in quantum cooperative systems. The method allows to determine rigorously existence, location, and exact form of separable ground…
Ground states of spin lattices can serve as a resource for measurement-based quantum computation. Ideally, the ability to perform quantum gates via measurements on such states would be insensitive to small variations in the Hamiltonian.…
We address the question of the classification of gapped ground states in one dimension that cannot be distinguished by a local order parameter. We introduce a family of quantum spin systems on the one-dimensional chain that have a unique…
This work provides an overview of gapped quantum spin systems, including concepts, techniques, properties, and results. The basic framework and objects of interest for quantum spin systems are introduced, and the main ideas behind methods…
The problem of estimating a generic phase-shift experienced by a quantum state is addressed for a generally degenerate phase shift operator. The optimal positive operator-valued measure is derived along with the optimal input state. Two…
After reviewing the role of phase in quantum mechanics, I discuss, with the aid of a number of unpublished documents, the development of quantum phase operators in the 1960's. Interwoven in the discussion are the critical physics questions…
We investigate global logarithmic asymptotics of ground states for a family of quantum mean field models. Our approach is based on a stochastic representation and a combination of large deviation and weak KAM techniques. The spin- 1/2 case…
The existence of definite orders in frustrated quantum systems is related rigorously to the occurrence of fully factorized ground states below a threshold value of the frustration. Ground-state separability thus provides a natural measure…