Related papers: Mathematical Theory for Quantum Phase Transitions
Lipkin model of arbitrary particle-number N is studied in terms of exact differential-operator representation of spin-operators from which we obtain the low-lying energy spectrum with the instanton method of quantum tunneling. Our new…
It has been demonstrated that the critical point of the phase transition in scalar quantum field theory with a quartic interaction in one space dimension can be approximated via a Gaussian Effective Potential (GEP). We discuss how this…
We introduce a group-theoretical extension of the Dicke model which describes an ensemble of two-level atoms interacting with a finite radiation field. The latter is described by a spin model whose main feature is that it possesses a…
We present a theory for the two kinds of dynamical quantum phase transitions, termed DPT-I and DPT-II, based on a minimal set of symmetry assumptions. In the special case of collective systems with infinite-range interactions, both are…
We propose a type of phase transition in quantum many-body systems, which occurs in highly excited quantum many-body scar states, while most of the spectrum is largely unaffected. Such scar state phase transitions can be realized by…
We introduce a framework for computing time-dependent quantum transition rates (QTRs) that describe the pace of evolution of a quantum state from a given subspace to a target subspace. QTRs are expressed in terms of flux-flux correlators…
We introduce and study dynamical probes of band structure topology in the post-quench time-evolution from mixed initial states of quantum many-body systems. Our construction generalizes the notion of dynamical quantum phase transitions…
We review the effects of excited-state quantum phase transitions (ESQPTs) in interacting many-body systems with finite numbers of collective degrees of freedom. We classify typical ESQPT signatures in the spectra of energy eigenstates with…
In this work we define a formal notion of a quantum phase crossover for certain Bethe ansatz solvable models. The approach we adopt exploits an exact mapping of the spectrum of a many-body integrable system, which admits an exact Bethe…
Dynamical quantum phase transitions can occur following quenches in quantum systems when the rate function, a dynamical analogue of the free energy, becomes non-analytic at critical times. Here we exhaustively investigate in an exemplary…
In this paper, we present an exactly solvable phase transition model in which the phase transition is purely statistically derived. The phase transition in this model is a generalized Bose-Einstein condensation. The exact expression of the…
Control landscape phase transitions (CLPTs) occur as abrupt changes in the cost function landscape upon varying a control parameter, and can be revealed by non-analytic points in statistical order parameters. A prime example are quantum…
A model of quantum measurement is proposed, which aims to describe statistical mechanical aspects of this phenomenon, starting from a purely Hamiltonian formulation. The macroscopic measurement apparatus is modeled as an ideal Bose gas, the…
We show that dynamic quantum phase transitions (DQPT) in many situations involve renormalization group (RG) fixed points that are unphysical in the context of thermal phase transitions. In such cases, boundary conditions are shown to become…
We explore the situation of intertwined quantum phase transitions (IQPTs), for which a QPT involving a crossing of two configurations is accompanied by a shape evolution of each configuration with its own separate QPT. We demonstrate the…
This study targets quantum phases which are characterized by topological properties and no associated with the symmetry breaking. We concern ourselves primarily with the transitions among these quantum phases. This type of quantum phase…
Quantum computation is based on implementing selected unitary transformations which represent algorithms. A generalized optimal control theory is used to find the driving field that generates a prespecified unitary transformation. The…
The dynamical quantum phase transition (DQPT) is an important concept in nonequilibrium critical phenomena; however, its relation to the equilibrium quantum phase transition (EQPT) remains obscure. Substantial evidence has suggested that…
In this talk, we briefly review the current understanding of the behavior of the QCD equation of state throughout the phase diagram. Special emphasis is given to regions of phenomenological interest, and a number of important open questions…
We calculate the quantum phase transition for a homogeneous Bose gas in the plane of s-wave scattering length a_s and temperature T. This is done by improving a one-loop result near the interaction-free Bose-Einstein critical temperature…