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0
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2answers
99 views

Example of gapped spin chain with degenerate ground space

What are the examples of a one dimensional spin chain, with local interaction and degenerate ground space (degeneracy may be a function of n, such as log(n) etc, where n is the length of chain) and a ...
10
votes
0answers
363 views

Lower bounds on spectral gaps of ferromagnetic spin-1/2 XXX Hamiltonians?

Question. Are there any references or techniques which can be applied to obtain energy gaps for ferromagnetic XXX spin-1/2 Hamitlonians, on general interaction graphs, or tree-graphs? I'm interested ...
8
votes
0answers
118 views

$\phi^4$ theory kinks as fermions?

In 1+1 dimensions there is duality between models of fermions and bosons called bosonization (or fermionization). For instance the sine-Gordon theory $$\mathcal{L}= \frac{1}{2}\partial_\mu \phi \...
2
votes
0answers
63 views

Anisotropic Hiesenberg model

I am reading the review article, "Quantum spin chains and Haldane gap" by I Affleck (http://iopscience.iop.org/article/10.1088/0953-8984/1/19/001/pdf). At one point of the discussion, he considers an ...
2
votes
0answers
48 views

A physical basis for Heisenberg ferromagnetic cluster model

Consider the following situation. There are $N$ spins 1/2 (for example 1/2, it may be any other value $s$) and they interact via the Hamiltonian: $$\hat{H}=-\sum_{i\neq j}\frac{J}{N}\hat{\vec{S}}_i \...
2
votes
0answers
126 views

Construction of a spin chain Hamiltonian invariant under a finite subgroup of SO(3)

I would like to construct a 2-local Hamiltonian that acts on a 1D spin chain where each spin transforms as the 3D irrep of $A_4$ which is a subgroup of $SO(3)$. I know that an $SO(3)$ invariant ...
2
votes
0answers
268 views

Spontaneous symmetry breaking in the quantum 1D XX model?

The ground states of the quantum 1D Ising and Heisenberg models exhibit spontaneous magnetization. Is this also true for the 1D XX model?
1
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0answers
44 views

Reference for open XX spin chain with external magnetic field

I would like a reference on the diagonalization of an open XX spin 1/2 chain with homogenous external magnetic field. I am new to the subject and I haven't been able to find a reference for it. Edit: ...
1
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0answers
51 views

How to expand free energy of Heisenberg spin chain?

In Dasgupta & Ma's 1979 paper "Low-temperature properties of the random Heisenberg antiferromagnetic chain", they give the free energy of a few interacting Heisenberg spins on a chain. I can't ...
1
vote
0answers
270 views

Fluctuation-Dissipation theorems in an infinite quantum system

So for a quantum spin chain, one can easily prove via the partition function that you have a fluctuation-dissipation type relation between the magnetic susceptibility and the variance of the ...
1
vote
0answers
150 views

What does it mean for a quantum spin chain to be “low energy”?

Is it another way of saying the ground state?
0
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0answers
45 views

At most $N$ gapless charge/spin modes in a system of $N$ coupled 1D chains?

Leon Balents and Matthew P. A. Fisher claimed the following without any further explanation ($N$ is the number of chains) For a system of $N$ coupled 1D chains, the number of gapless charge modes ...