scholarly journals Relaxation of the order-parameter statistics in the Ising quantum chain

2019 ◽  
Vol 7 (6) ◽  
Author(s):  
Mario Collura
Keyword(s):  
Probability Distribution ◽  
Ground State ◽  
Order Parameter ◽  
Classical Model ◽  
Transverse Field ◽  
Analytical Description ◽  
Spin Correlation ◽  
Local Order ◽  
Late Time ◽  
Quantum Chain

We study the out-of-equilibrium probability distribution function of the local order parameter in the transverse field Ising quantum chain. Starting from a fully polarised state, the relaxation of the ferromagnetic order is analysed: we obtain a full analytical description of the late-time stationary distribution by means of a remarkable relation to the partition function of a 3-states classical model. Accordingly, depending on the phase whereto the post-quench Hamiltonian belongs, the probability distribution may locally retain memories of the initial long-range order. When quenching deep in the broken-symmetry phase, we show that the stationary order-parameter statistics is indeed related to that of the ground state. We highlight this connection by inspecting the ground-state equilibrium properties, where we propose an effective description based on the block-diagonal approximation of the nn-point spin correlation functions.

scholarly journals Quantum criticality in dimerised anisotropic spin-1 chains

2021 ◽  
Author(s):  
Satoshi Ejima ◽  
Florian Lange ◽  
Holger Fehske
Keyword(s):  
Phase Transition ◽  
Ground State ◽  
Order Parameter ◽  
Central Charge ◽  
Universality Class ◽  
Spin Correlation ◽  
Quantum Criticality ◽  
Ground State Phase Diagram ◽  
Spin Correlation Function ◽  
Theoretical Predictions

AbstractApplying the (infinite) density-matrix renormalisation group technique, we explore the effect of an explicit dimerisation on the ground-state phase diagram of the spin-1 XXZ chain with single-ion anisotropy D. We demonstrate that the Haldane phase between large-D and antiferromagnetic phases survives up to a critical dimerisation only. As a further new characteristic the dimerisation induces a direct continuous Ising quantum phase transition between the large-D and antiferromagnetic phases with central charge $$c=1/2$$ c = 1 / 2 , which terminates at a critical end-point where $$c=7/10$$ c = 7 / 10 . Calculating the critical exponents of the order parameter, neutral gap and spin–spin-correlation function, we find $$\beta =1/8$$ β = 1 / 8 (1/24), $$\nu =1$$ ν = 1 (5/9), and $$\eta =1/4$$ η = 1 / 4 (3/20), respectively, which proves the Ising (tricritical Ising) universality class in accordance with field-theoretical predictions.

Order, Symmetry, and the Organization of Matter

2013 ◽  
Author(s):  
Daniel L. Stein ◽  
Charles M. Newman
Keyword(s):  
Phase Transition ◽  
Statistical Mechanics ◽  
Ground State ◽  
Order Parameter ◽  
Condensed Matter ◽  
Broken Symmetry ◽  
Essential Ingredient ◽  
Important Concept ◽  
Basic Concepts ◽  
Thermodynamics And Statistical Mechanics

This chapter introduces the basic concepts and language that will be needed later on: order, symmetry, invariance, broken symmetry, Hamiltonian, condensed matter, order parameter, ground state, and several thermodynamic terms. It also presents the necessary concepts from thermodynamics and statistical mechanics that will be needed later. It boils down the latter to its most elemental and essential ingredient: that of temperature as controlling the relative probabilities of configurations of different energies. For much of statistical mechanics, all else is commentary. This is sufficient to present an intuitive understanding of why and how matter organizes itself into different phases as temperature varies, and leads to the all-important concept of a phase transition.

Detecting chimeras by eigenvalue decomposition of the bivariate local order parameter

2020 ◽  
Vol 130 (2) ◽  
pp. 28003
Author(s):  
Fatemeh Parastesh ◽  
Hamed Azarnoush ◽  
Sajad Jafari ◽  
Matjaž Perc
Keyword(s):  
Order Parameter ◽  
Eigenvalue Decomposition ◽  
Local Order ◽  
Local Order Parameter

MODULATION OF ORDER PARAMETER OF EXCITON BOSE-EINSTEIN CONDENSATE IN A RING

2004 ◽  
Vol 18 (27n29) ◽  
pp. 3797-3802 ◽  
Author(s):  
S.-R. ERIC YANG ◽  
Q-HAN PARK ◽  
J. YEO
Keyword(s):  
Ground State ◽  
Order Parameter ◽  
Weak Magnetic Field ◽  
Random Potential ◽  
Einstein Condensate ◽  
Einstein Condensation ◽  
Random Potentials ◽  
Bose Einstein Condensate ◽  
The Mean ◽  
Bose Einstein

We have studied theoretically the Bose-Einstein condensation (BEC) of two-dimensional excitons in a ring with a random variation of the effective exciton potential along the circumference. We derive a nonlinear Gross-Pitaevkii equation (GPE) for such a condensate, which is valid even in the presence of a weak magnetic field. For several types of the random potentials our numerical solution of the ground state of the GPE displays a necklace-like structure. This is a consequence of the interplay between the random potential and a strong nonlinear repulsive term of the GPE. We have investigated how the mean distance between modulation peaks depends on properties of the random potentials.

Ground-state energy of a quantum chain with competing interactions

1995 ◽  
Vol 79 (1-2) ◽  
pp. 347-376 ◽  
Author(s):  
C. E. I. Carneiro ◽  
M. J. de Oliveira ◽  
W. F. Wreszinski
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Competing Interactions ◽  
Quantum Chain

Effect of spin correlation on133Cs nuclear magnetic relaxation in singlet ground state system CsFeCl3

1996 ◽  
Vol 46 (S4) ◽  
pp. 2087-2088
Author(s):  
Mitsuru Toda ◽  
Tomoyuki Sadakane ◽  
Takao Goto ◽  
Meirou Chiba ◽  
Kimio Adachi
Keyword(s):  
Ground State ◽  
Magnetic Relaxation ◽  
Spin Correlation ◽  
Nuclear Magnetic Relaxation ◽  
State System ◽  
Singlet Ground State ◽  
Nuclear Magnetic

scholarly journals Local disorder, topological ground state degeneracy and entanglement entropy, and discrete anyons

2017 ◽  
Vol 29 (06) ◽  
pp. 1750018 ◽  
Author(s):  
Sven Bachmann
Keyword(s):  
Ground State ◽  
Entanglement Entropy ◽  
Orientable Surface ◽  
Cell Complex ◽  
Local Order ◽  
Topological Order ◽  
Cohomology Groups ◽  
Closed Orientable Surface ◽  
Ground State Degeneracy ◽  
Comprehensive Study

In this comprehensive study of Kitaev’s abelian models defined on a graph embedded on a closed orientable surface, we provide complete proofs of the topological ground state degeneracy, the absence of local order parameters, compute the entanglement entropy exactly and characterize the elementary anyonic excitations. The homology and cohomology groups of the cell complex play a central role and allow for a rigorous understanding of the relations between the above characterizations of topological order.

Sign in / Sign up

Export Citation Format

Share Document