Related papers: Quantum Symmetry on Potts Model
Using Monte Carlo simulations in the frame of stochastic series expansion (SSE), we study the three-state quantum Potts model. The cluster algorithm we used is a direct generalization of that for the quantum Ising model. The simulations…
The practical use of non-Hermitian (i.e., typically, PT-symmetric) phenomenological quantum Hamiltonians is discussed as requiring an explicit reconstruction of the {\em ad hoc} Hilbert-space metrics which would render the time-evolution…
We consider a constructive modification of quantum-mechanical formalism. Replacement of a general unitary group by unitary representations of finite groups makes it possible to reproduce quantum formalism without loss of its empirical…
A geometric interpretation of the spontaneous symmetry breaking effect, which plays a key role in the Standard Model, is developed. The advocated approach is related to the effective use of the momentum 4-spaces of the constant curvature,…
The observation of genuine quantum effects in systems governed by non-Hermitian Hamiltonians has been an outstanding challenge in the field. Here we simulate the evolution under such Hamiltonians in the quantum regime on a superconducting…
Quantum groups play the role of hidden symmetries of some two-dimensional field theories. We discuss how they appear in this role in the Wess-Zumino-Witten model of conformal field theory.
Outer automorphisms of symmetries ("symmetries of symmetries") in relativistic quantum field theories are studied, including charge conjugation (C), space-reflection (P) , and time-reversal (T) transformations. The group theory of outer…
The Fourier transform, known in classical analysis, and generalized in abstract harmonic analysis, can also be considered in the theory of locally compact quantum groups. In this note, I discuss some aspects of this more general Fourier…
In this letter we present a theorem on the dynamics of the generalized Hubbard models. This theorem shows that the symmetry of the single particle Hamiltonian can protect a kind of dynamical symmetry driven by the interactions. Here the…
Essential properties of semiclassical approximation for quantum mechanics are viewed as axioms of an abstract semiclassical mechanics. Its symmetry properties are discussed. Semiclassical systems being invariant under Lie groups are…
Connecting ideas of geometric formulation of quantum mechanics with new results in symplectic geometry a new approach to geometrical quantization procedure is proposed. As a first result we verify that the correspondence between "classical"…
We discuss the the notion of a partial dynamical symmetry (PDS), for which a prescribed symmetry is obeyed by only a subset of solvable eigenstates, while other eigenstates are strongly mixed. We present an explicit construction of…
We describe a semidefinite relaxation method which finds lower bounds to the ground state energy of a quantum Hamiltonian subject to Hermitian linear constraints along with approximations of ground state expectation values. We show that…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
Spontaneous symmetry breaking in systems with symmetry is a cornerstone phenomenon accompanying second-order phase transitions. Here, we predict the opposite phenomenon, namely, spontaneous symmetry emergence in a system that lacks…
It was recently argued that quantum field theories possess one-form and higher-form symmetries, labelled `generalized global symmetries.' In this paper, we describe how those higher-form symmetries can be understood mathematically as…
Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner…
We study a quantum mechanical toy model that mimics some features of a quenched phase transition. Both by virtue of a time-dependent Hamiltonian or by changing the temperature of the bath we are able to show that even after classicalization…
The catastrophe theory is applied to a nuclear cluster model and an effective model for QCD at low energy. The study of quantum phase transitions in the cluster model was considered in an earlier publication, but restricted to spherical…
Dependent symmetries, symmetries that depend on the situation of the subsystem in a larger closed system, are explored by looking at simple examples. This is a new kind of symmetry in the open quantum dynamics of a subsystem Each symmetry…