Particles, holes and solitons: a matrix product state approach (original) (raw)

Low-energy effective quantum field theoretic description of excitations about soliton configurations

Annals of Physics, 2021

Solitons are the classical field configurations connecting two trivial vacua. These are also the solutions of classical field equations of motion with particle-like properties. Moreover, they are localized in space, having finite energy, and are stable against decay into radiation. The coherent state description of kink-solitons is discussed in the present article. Further, the relation between topological solitons and occupation numbers corresponding to low momentum excitations are also discussed coherently. The description of the low energy excitations about solitons in quantum field theory is the main theme of this article. Further, a few physical observables, namely some low order correlation functions, are computed up to certain integral forms. Furthermore, we have shown that it is possible to detect the presence of soliton-like classical configurations in many-particle systems from the nature of the one-point function and non-conservation of momentum feature of one-point, two-point and three-point functions in this low-energy effective field theory of these excitations.

Soliton quantization in lattice field theories

Communications in Mathematical Physics, 1987

Quantization of solitons in terms of Euclidean region functional integrals is developed, and Osterwalder-Schrader reconstruction is extended to theories with topological solitons. The quantization method is applied to several lattice field theories with solitons, and the particle structure in the soliton sectors of such theories is analyzed. A construction of magnetic monopoles in the fourdimensional, compact t/(l)-model, in the QED phase, is indicated as well.

Soliton mass and surface tension in the (λ|Ø|4)2 quantum field model

Communications in Mathematical Physics, 1978

The spectrum of the mass operator on the soliton sectors of the anisotropic (2lq~14)2--and the (2q~4)2~quantum field models in the two phase region is analyzed. It is proven that, for small enough ,~. >0, the mass gap m~(2) on the soliton sector is positive, and m~()0=0(2-1). This involves estimating m,(2) from below by a quantity z(2) analogous to the surface tension in the statistical mechanics of two dimensional, classical spin systems and then estimating z(2) by methods of Euclidean field theory. In principle, our methods apply to any two dimensional quantum field model with a spontaneously broken, internal symmetry group.

Generalized route to effective field theories for quantum systems with local constraints

Physical Review B

Some of the exciting phenomena uncovered in strongly correlated systems in recent years -for instance quantum topological order, deconfined quantum criticality and emergent gauge symmetries -appear in systems where the Hilbert space is effectively projected at low energies in a way that imposes local constraints on the original degrees of freedom. Cases in point include spin liquids, valence bond systems, dimer and vertex models. In this work, we use a slave boson description coupled to a large-S path integral formulation to devise a generalised route to obtain effective field theories for such systems. We demonstrate the validity and capability of our approach by studying quantum dimer models and by comparing our results with the existing literature. Field theoretic approaches to date are limited to bipartite lattices, they depend on a gauge-symmetric understanding of the constraint, and lack generic quantitative predictive power for the coefficients of the terms that appear in the Lagrangians of these systems. Our method overcomes all these shortcomings and we show how the results up to quadratic order compare with the known height description of the square lattice quantum dimer model, as well as with the numerical estimate of the speed of light of the photon excitations on the diamond lattice. Finally, instanton considerations allow us to infer properties of the finite temperature behaviour in two dimensions.

Variational Approach to Strong Coupling Field Theory* I. $4 Theory

Theoretical attempts to understand hadrons in terms of confined quark con- stituents lead naturally to the study of quantum field theory with methods that can be applied when strong interactions are present. In this paper nonperturba- tive, variational techniques are developed and applied to calculating the ground state and low lying collective excitations (lfkinks*') of theories rendered finite on a discrete lattice. Particular application is made to a scalar theory with a self- coupling of the form A( $2 - f2) 2 in two dimensions. Working in configuration space we reduce the theory to coupled Schrddinger problems and establish the conditions for the variational solution to exhibit a phase transition between ground states with <4> = 0 and those exhibiting a spontaneously broken symmetry such that <+> # 0. The phase transition is a second-order one in a simple trial state con- structed in a single-site product basis. Low lying excitations are constructed that are an...

Correspondence between dark solitons and the type II excitations of the Lieb-Liniger model

Physical Review A, 2015

A one-dimensional model of bosons with repulsive short-range interactions, solved analytically by Lieb and Liniger many years ago, predicts existence of two branches of elementary excitations. One of them represents Bogoliubov phonons, the other, as suggested by some authors, might be related to dark solitons. On the other hand, it has been already demonstrated within a framework of the classical field approximation that quasi-one-dimensional interacting Bose gas at equilibrium exhibits excitations which are phonons and dark solitons. By showing that statistical distributions of dark solitons obtained within the classical field approximation match the distributions of quasiparticles of the second kind derived from fully quantum description we demonstrate that type II excitations in the Lieb-Liniger model are, indeed, quantum solitons.

Lieb-Robinson Bound and the Butterfly Effect in Quantum Field Theories

Physical review letters, 2016

As experiments are increasingly able to probe the quantum dynamics of systems with many degrees of freedom, it is interesting to probe fundamental bounds on the dynamics of quantum information. We elaborate on the relationship between one such bound-the Lieb-Robinson bound-and the butterfly effect in strongly coupled quantum systems. The butterfly effect implies the ballistic growth of local operators in time, which can be quantified with the "butterfly" velocity v_{B}. Similarly, the Lieb-Robinson velocity places a state-independent ballistic upper bound on the size of time evolved operators in nonrelativistic lattice models. Here, we argue that v_{B} is a state-dependent effective Lieb-Robinson velocity. We study the butterfly velocity in a wide variety of quantum field theories using holography and compare with free-particle computations to understand the role of strong coupling. We find that v_{B} remains constant or decreases with decreasing temperature. We also comme...

Variational Approach to Strong Coupling Field Theory. 1. φ 4 Theory, Phys. Rev. D14

1976

Theoretical attempts to understand hadrons in terms of confined quark con-stituents lead naturally to the study of quantum field theory with methods that can be applied when strong interactions are present. In this paper nonperturba-tive, variational techniques are developed and applied to calculating the ground state and low lying collective excitations (lfkinks*‘) of theories rendered finite on a discrete lattice. Particular application is made to a scalar theory with a self-coupling of the form A ( $2- f2) 2 in two dimensions. Working in configuration space we reduce the theory to coupled Schrddinger problems and establish the conditions for the variational solution to exhibit a phase transition between ground states with <4> = 0 and those exhibiting a spontaneously broken symmetry such that <+> # 0. The phase transition is a second-order one in a simple trial state con-structed in a single-site product basis. Low lying excitations are constructed that are analogues o...