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17
votes
1answer
176 views

Fluctuations of an interface with hammock potential

This question is related to that one. I ask it here since comments are too short for the extended discussion that was going on there. I am interested in a very simple interface model. To each ...
1
vote
0answers
25 views

Topological S-matrix as an operator in the graphical calculus

My question comes from the following classic paper by Kitaev: Anyons in an exactly solved model and beyond (arXiv link) In Appendix E (pg 86), Kitaev introduces a diagram operator $S_z$ which acts ...
0
votes
0answers
45 views

Frustrated Heisenberg XXZ Model

At the moment, I am look at the frustrated XXZ Heisenberg model, given by the Hamiltonian \begin{align} H=\sum_{i=1}^N\left(J_1S_i^Z S_{i+1}^Z+J_1'\frac{1}{2}(S_i^+S_{i+1}^-+S_i^-S_{i+1}^+)+J_2S_i^Z ...
1
vote
1answer
52 views

Why is the ground state energy of the Heisenberg XXZ Model unbounded for some values of $J$?

At the moment, I'm looking at numerically studying the Heisenberg XXZ model. The Hamiltonian is given below: $$ H=\sum_{j=1}^{N-1}\left(J S_j^z ...
0
votes
1answer
96 views

Monte carlo simulation for continuous spin model (e.g. XY or Heisenberg model)

Unlike the Ising model, the XY model and the Heisenberg model have a continuous spectrum. So one need discretize them for a numerical simulation. But how to make sure the discretization procedure ...
3
votes
2answers
681 views

Nuclear Spin of Sodium 23

I am actually calculating the nuclear spin of Sodium 23. Here we have 11 protons and 12 neutrons. Now both the nuclei are short of the magic numbers. When I use the shell model for protons and ...
1
vote
1answer
90 views

A puzzle of thermalization in simulating the 3D XY-model

I am learning the classical Monte Carlo simulation. When I simulate the 3D XY-model $$ \beta H = -\beta J \sum_{<i,j>} cos(\theta_i-\theta_j) $$ where $\beta$ is the inverse of the temperature ...
2
votes
1answer
68 views

Does the q-states Potts become the XY model in large q state?

I have met several times in papers, the order of the phase transition of the $q$-state Potts model depends on $q$. E.g., in two dimensions, for $q = 2$ (the Ising model), $3$, $4$ the order-disorder ...
1
vote
3answers
58 views

What is spin on a lattice site is it electrons or atom as a whole?

Hi I wanted to know what is spin half in lattice site means? Is it electron or atom or total spins half of electrons in a atomic 1d chain or 2d?
2
votes
1answer
62 views

What is a 'height field'?

I encountered a few times the expression of 'height fields' in statistical physics, without ever reading a proper definition. My textbooks don't seem to talk about that, and googling it hasn't been ...
3
votes
1answer
204 views

Definition for Chiral Spin Liquid

What is the definition of chiral spin liquid? Especially what does chiral mean here? I encounter a lot of terminologies with chiral. It seems they mean differently in different contexts. If you could ...
1
vote
0answers
62 views

What is the minimal symmetry required for a spin Hamiltonian to describe a spin-liquid ground state?

Let's restrict to the case of spin-1/2 system. As we know, a spin-liquid (SL) state is the ground state of a lattice spin Hamiltonian with no spontaneous broken symmetries (sometime it may ...
4
votes
1answer
627 views

A simple model that exhibits emergent symmetry?

In a previous question Emergent symmetries I asked, Prof.Luboš Motl said that emergent symmetries are never exact. But I wonder whether the following example is an counterexample that has exact ...
3
votes
1answer
748 views

Some limiting cases of the Heisenberg XXZ model (2/2)

NOTE: Because this was a long question I have split it up in two different questions! For a course on quantum integrability I am reading these notes. (Franchini: Notes on Bethe Ansatz Techniques. ...
3
votes
1answer
129 views

Chiral Spin Liquid(CSL), Chern number, and the ground state degeneracy(GSD)

Consider a 2D gapped CSL with a nonzero Chern number $m$, then is the GSD of the system on a torus directly related to the Chern number $m$? For example, see this article, in the last paragraph on ...
1
vote
1answer
79 views

What is the universality class of transition in one-dimensional XXZ Heisenberg at $\Delta$ = -1?

In the one-dimensional spin-$\frac12$ XXZ Heisenberg model, $$H=J\sum_i{S_i^x S_{i+1}^x + S_i^y S_{i+1}^y+\Delta S_i^z S_{i+1}^z},$$ with $J>0$. There are two transition points: $\Delta=1$ ...
1
vote
0answers
51 views

Find out ground sates for large 2D classical spin model

Reaching the ground state of a large 2D classical spin model (e.g. classical Heisenberg model) might be a relatively difficult task while using conventional "flip/reject" Monte Carlo method. The ...
5
votes
1answer
300 views

Magnetic monopoles in spin ice and Dirac string comparison

In spin ice systems magnetic monopole-like excitations are sources or sinks of $H$, not the $B$ field, why is that? Is it because the strings carries magnetic moment $M$ and not solenoidal $B$ filed ...
0
votes
0answers
137 views

A simple question on the projected wave function?

For example, consider a spin-1/2 AFM Heisenberg Hamiltonian $H=\sum_{<ij>}\mathbf{S}_i\cdot\mathbf{S}_j$, and we perform a ...
3
votes
1answer
83 views

How do we determine the statistics and spin of quasi-particles?

I am considering the Heisenberg XXZ model at the moment. In the literature it says that (in the $J\Delta\rightarrow\infty$ limit, i.e. the ferromagnetic Ising regime) one can either view low-energy ...
1
vote
1answer
438 views

Some limiting cases of the Heisenberg XXZ model (1/2)

NOTE: Because this was a long question I have split it up in two different questions! For a course on quantum integrability I am reading these notes. (Franchini: Notes on Bethe Ansatz Techniques. ...
0
votes
1answer
77 views

Adiabatic quantum Hamiltonian of variable dimension

Is adiabatic quantum Hamiltonian of variable dimension possible? This is very hypothetical and I am afraid may not have enough merit to belong to this forum. I would still like to elaborate. Here is ...
2
votes
0answers
50 views

Spin Transition Energies

I am reading a paper: http://arxiv.org/ftp/arxiv/papers/1305/1305.2445.pdf On p. 22, the following Hamiltonian is given: $$ H = \mu_B g \mathbf{B} \cdot \mathbf{S} + D(S_Z^2+\frac{1}{3}S(S+1)) + ...
2
votes
1answer
68 views

Elastic vs Inelastic vs isospin violating scattering particle physics models

I'm looking for a nice paper that explains the difference between three particle physics models for spin-independent dark matter interaction with nuclei: elastic, inelastic and isospin violating ...
2
votes
2answers
391 views

Long Range Spin-Spin Interactions

A recent article on probing Earth's interior mentioned the potential use of a "fifth force", long range electron spin-spin interactions, as a tool in the endeavor. Has anybody published any ...
8
votes
1answer
87 views

Many body quantum states analyzed as probabilistic sequences

Measurements of consecutive sites in a many body qudit system (e.q. a spin chain) can be interpreted as generating a probabilistic sequence of numbers $X_1 X_2 X_3 \ldots$, where $X_i\in ...
3
votes
1answer
864 views

Why we call the ground state of Kitaev model a Spin Liquid?

Now we always talk about the so-called Kitaev spin liquid. One important property of spin liquid is global spin rotation symmetry. Let $\Psi$ represents a spin ground state, if $\Psi$ has global spin ...
2
votes
1answer
79 views

What is the physical meaning of this simplification to calculate the effective coupling constants for a Gaussian model with quartic interactions?

To calculate the effective coupling constants $u'_2(q)$ and $u'_4(q)$ of the effective Hamiltinian eq (4.9) of this paper $$ H' = -\frac{1}{2}\int\limits_q u'_2(q)\sigma'_q\sigma'_{-q} - ...
3
votes
1answer
120 views

Random bond Ising model and computational efficiency

If you want to find the ground state of the 2d random bond Ising model (no field), a computationally efficient algorithm exists to do it for you (based on minimum weight perfect matching). What about ...
4
votes
2answers
130 views

Do any entanglement measures for mixed states exist that use only single site correlation functions?

For a pure state $\rho_{AB}$, the entropy of entanglement of subsystem $A$ is \begin{equation} S( \rho_A) = -tr (\rho_A \log \rho_A) \end{equation} where $\rho_A$ is the reduced density matrix of A. ...
7
votes
1answer
133 views

How does one geometrically quantize the Bloch equations?

I've just now rated David Bar Moshe's post (below) as an "answer", for which appreciation and thanks are given. Nonetheless there's more to be said, and in hopes of stimulating further posts, I've ...
14
votes
1answer
138 views

Phase Transition in the Ising Model with Non-Uniform Magnetic Field

Consider the Ferromagnetic Ising Model ($J>0$) on the lattice $\mathbb{Z}^2$ with the Hamiltonian with boundary condition $\omega\in\{-1,1\}$ formally given by $$ ...
12
votes
3answers
150 views

Visualization of 1D spin chain wave fuction

What are the known methods for visualizing quantum states of one-dimensional spin chains? They can be based either on their wave functions or density matrices. My particular interest is in plotting ...
7
votes
0answers
69 views

Do bipartite spin glasses have simple relaxation dynamics?

From what I gather, a Boltzmann machine (BM) is essentially a spin glass with no applied field evolving under Glauber dynamics (if this is at all mistaken, I don't think it will be off enough to ...
22
votes
1answer
408 views

Mermin-Wagner theorem in the presence of hard-core interactions

It seems quite common in the theoretical physics literature to see applications of the "Mermin-Wagner theorem" (see wikipedia or scholarpedia for some limited background) to systems with hard-core ...