scholarly journals Dimerization in Quantum Spin Chains with O(n) Symmetry

2021 ◽  
Author(s):  
Jakob E. Björnberg ◽  
Peter Mühlbacher ◽  
Bruno Nachtergaele ◽  
Daniel Ueltschi
Keyword(s):  
Phase Diagram ◽  
Ground State ◽  
Quantum Spin ◽  
Spin Chains ◽  
Dimensional System ◽  
Quantum Spin Chains ◽  
One Dimensional ◽  
Open Region ◽  
Quantum Spins ◽  
The One

AbstractWe consider quantum spins with $$S\ge 1$$ S ≥ 1 , and two-body interactions with $$O(2S+1)$$ O ( 2 S + 1 ) symmetry. We discuss the ground state phase diagram of the one-dimensional system. We give a rigorous proof of dimerization for an open region of the phase diagram, for S sufficiently large. We also prove the existence of a gap for excitations.

scholarly journals MARKOVIAN KMS-STATES FOR ONE-DIMENSIONAL SPIN CHAINS

1999 ◽  
Vol 02 (04) ◽  
pp. 645-661 ◽  
Author(s):  
LUIGI ACCARDI ◽  
VOLKMAR LIEBSCHER
Keyword(s):  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Kms States ◽  
One Dimensional ◽  
Locality Property ◽  
Conditional Expectations ◽  
Starting Point ◽  
Modular Automorphism ◽  
Quantum Spin Lattices

We characterize a class of quantum Markov states in terms of a locality property of their modular automorphism group or, equivalently, of their φ-conditional expectations and we give an explicit description of the structure of these states. This study is meant as a starting point for the investigation of the structure of Markovian KMS-states of quantum spin chains as well as of multidimensional quantum spin lattices.

Quantum mechanics of the damped harmonic oscillator

2002 ◽  
Vol 80 (6) ◽  
pp. 645-660 ◽  
Author(s):  
M Blasone ◽  
P Jizba
Keyword(s):  
Harmonic Oscillator ◽  
Ground State ◽  
Geometric Phase ◽  
State Energy ◽  
Dimensional System ◽  
One Dimensional ◽  
Damped Harmonic Oscillator ◽  
Linear Harmonic Oscillator ◽  
Two Dimensional System ◽  
The One

We quantize the system of a damped harmonic oscillator coupled to its time-reversed image, known as Bateman's dual system. By using the Feynman–Hibbs method, the time-dependent quantum states of such a system are constructed entirely in the framework of the classical theory. The geometric phase is calculated and found to be proportional to the ground-state energy of the one-dimensional linear harmonic oscillator to which the two-dimensional system reduces under appropriate constraint. PACS Nos.: 03.65Ta, 03.65Vf, 03.65Ca, 03.65Fd

RENORMALIZATION-GROUP INVESTIGATION OF THE S = 1 RANDOM ANTIFERROMAGNETIC HEISENBERG CHAIN

2006 ◽  
Vol 17 (12) ◽  
pp. 1739-1753 ◽  
Author(s):  
PÉTER LAJKÓ
Keyword(s):  
Phase Diagram ◽  
Renormalization Group ◽  
Density Matrix ◽  
Energy Scale ◽  
Quantum Spin ◽  
Spin Chains ◽  
Density Matrix Renormalization Group ◽  
Heisenberg Chain ◽  
Quantum Spin Chains ◽  
Density Matrix Renormalization

We introduce variants of the Ma-Dasgupta renormalization-group (RG) approach for random quantum spin chains, in which the energy-scale is reduced by decimation built on either perturbative or non-perturbative principles. In one non-perturbative version of the method, we require the exact invariance of the lowest gaps, while in a second class of perturbative Ma-Dasgupta techniques, different decimation rules are utilized. For the S = 1 random antiferromagnetic Heisenberg chain, both type of methods provide the same type of disorder dependent phase diagram, which is in agreement with density-matrix renormalization-group calculations and previous studies.

scholarly journals Universal emergence of the one-third plateau in the magnetization process of frustrated quantum spin chains

2007 ◽  
Vol 75 (6) ◽  
Author(s):  
F. Heidrich-Meisner ◽  
I. A. Sergienko ◽  
A. E. Feiguin ◽  
E. R. Dagotto
Keyword(s):  
Quantum Spin ◽  
Spin Chains ◽  
Magnetization Process ◽  
Quantum Spin Chains ◽  
The One
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