scholarly journals Generalized Gibbs Phase Rule and Multicriticality Applied to Magnetic Systems

Entropy ◽  
2021 ◽  
Vol 24 (1) ◽  
pp. 63
Author(s):  
Daniele A. Dias ◽  
Francisco W. S. Lima ◽  
Joao A. Plascak
Keyword(s):  
Ground State ◽  
Degrees Of Freedom ◽  
Good Description ◽  
Phase Rule ◽  
Magnetic Systems ◽  
Gibbs Phase Rule ◽  
Spin Hamiltonians ◽  
Multicritical Points ◽  
Ground State Degeneracy ◽  
General Phase

A generalization of the original Gibbs phase rule is proposed in order to study the presence of single phases, multiphase coexistence, and multicritical phenomena in lattice spin magnetic models. The rule is based on counting the thermodynamic number of degrees of freedom, which strongly depends on the external fields needed to break the ground state degeneracy of the model. The phase diagrams of some spin Hamiltonians are analyzed according to this general phase rule, including general spin Ising and Blume–Capel models, as well as q-state Potts models. It is shown that by properly taking into account the intensive fields of the model in study, the generalized Gibbs phase rule furnishes a good description of the possible topology of the corresponding phase diagram. Although this scheme is unfortunately not able to locate the phase boundaries, it is quite useful to at least provide a good description regarding the possible presence of critical and multicritical surfaces, as well as isolated multicritical points.

scholarly journals A degeneracy bound for homogeneous topological order

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Jeongwan Haah
Keyword(s):  
Riemannian Manifold ◽  
Linear Transformation ◽  
Ground State ◽  
Degrees Of Freedom ◽  
Lattice Spacing ◽  
Topological Order ◽  
Closed Riemannian Manifold ◽  
Ground State Degeneracy ◽  
Quantum Spins ◽  
Isometry Class

We introduce a notion of homogeneous topological order, which is obeyed by most, if not all, known examples of topological order including fracton phases on quantum spins (qudits). The notion is a condition on the ground state subspace, rather than on the Hamiltonian, and demands that given a collection of ball-like regions, any linear transformation on the ground space be realized by an operator that avoids the ball-like regions. We derive a bound on the ground state degeneracy \mathcal D𝒟 for systems with homogeneous topological order on an arbitrary closed Riemannian manifold of dimension dd, which reads [ D c (L/a)^{d-2}.] Here, LL is the diameter of the system, aa is the lattice spacing, and cc is a constant that only depends on the isometry class of the manifold, and \muμ is a constant that only depends on the density of degrees of freedom. If d=2d=2, the constant cc is the (demi)genus of the space manifold. This bound is saturated up to constants by known examples.examples.

scholarly journals Exact mapping between a laser network loss rate and the classical XY Hamiltonian by laser loss control

Nanophotonics ◽  
2020 ◽  
Vol 9 (13) ◽  
pp. 4117-4126 ◽  
Author(s):  
Igor Gershenzon ◽  
Geva Arwas ◽  
Sagie Gadasi ◽  
Chene Tradonsky ◽  
Asher Friesem ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Loss Rate ◽  
Oscillation Amplitude ◽  
Xy Model ◽  
Spin Hamiltonian ◽  
Laser Oscillator ◽  
Physical Systems ◽  
Network State ◽  
Spin Hamiltonians ◽  
Loss Control

AbstractRecently, there has been growing interest in the utilization of physical systems as heuristic optimizers for classical spin Hamiltonians. A prominent approach employs gain-dissipative optical oscillator networks for this purpose. Unfortunately, these systems inherently suffer from an inexact mapping between the oscillator network loss rate and the spin Hamiltonian due to additional degrees of freedom present in the system such as oscillation amplitude. In this work, we theoretically analyze and experimentally demonstrate a scheme for the alleviation of this difficulty. The scheme involves control over the laser oscillator amplitude through modification of individual laser oscillator loss. We demonstrate this approach in a laser network classical XY model simulator based on a digital degenerate cavity laser. We prove that for each XY model energy minimum there corresponds a unique set of laser loss values that leads to a network state with identical oscillation amplitudes and to phase values that coincide with the XY model minimum. We experimentally demonstrate an eight fold improvement in the deviation from the minimal XY energy by employing our proposed solution scheme.

Anyon representation of the ground-state degeneracy of the quantum frustratedXYmodel

1992 ◽  
Vol 45 (10) ◽  
pp. 5737-5739 ◽  
Author(s):  
Maria Cristina Diamantini ◽  
Pasquale Sodano
Keyword(s):  
Ground State ◽  
Ground State Degeneracy

scholarly journals Boundary states for chiral symmetries in two dimensions

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Philip Boyle Smith ◽  
David Tong
Keyword(s):  
Boundary Conditions ◽  
Ground State ◽  
Zero Mode ◽  
Central Charge ◽  
Two Dimensions ◽  
Dirac Fermions ◽  
Chiral Symmetries ◽  
Boundary States ◽  
Ground State Degeneracy ◽  
Left And Right

Abstract We study boundary states for Dirac fermions in d = 1 + 1 dimensions that preserve Abelian chiral symmetries, meaning that the left- and right-moving fermions carry different charges. We derive simple expressions, in terms of the fermion charge assignments, for the boundary central charge and for the ground state degeneracy of the system when two different boundary conditions are imposed at either end of an interval. We show that all such boundary states fall into one of two classes, related to SPT phases supported by (−1)F , which are characterised by the existence of an unpaired Majorana zero mode.

Mesonic and isobar degrees of freedom in the ground state of the nuclear many-body system

1978 ◽  
Vol 18 (5) ◽  
pp. 2416-2429 ◽  
Author(s):  
M. R. Anastasio ◽  
Amand Faessler ◽  
H. Müther ◽  
K. Holinde ◽  
R. Machleidt
Keyword(s):  
Ground State ◽  
Degrees Of Freedom ◽  
Body System ◽  
Many Body
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