# Questions tagged [spin-chains]

One dimensional quantum systems which can either be multiple discrete spin particles or their continuum limit.

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### Spin Chains - Why are eigenstates always expressed in the z-basis

I was wondering why when we have spin chain Hamiltonians, like the Heisenberg model, we always express the eigenstates in the spin z- eigenbasis. Or maybe, I could pose my question this way - to be ...
854 views

### What is the relation between spin waves, the Haldane gap, and a spin-1 chain?

I know that a spin wave occurs when a magnetic moment is deflected from its equilibrium position. The deflected magnetic moment will process around its equilibrium axis. Additionally, the Haldane ...
40 views

### Example of spin chains with finite-lifetime quasi-particles?

Does anyone know a one-dimensional spin model where the low-energy excitations have a finite lifetime? (E.g. in terms of the spectral function $\mathcal S(k, \omega)$ this means one would get a finite ...
44 views

### Change in ground state after perturbing a hamiltonian

Lets consider a spin $\frac{1}{2}$ chain with $n$ spins and an associated local hamiltonian $H= \sum_i h_{i,i+1}$. We also assume that $\|h_{i,i+1}\|_{\infty} \leq 1$. In this question, we will be ...
33 views

### How to compute the MPS representation for a sequence of asymptotically gapped quantum spin chains

Suppose I have a sequence of gapped, spin-$1/2$, translationally invariant quantum spin chains $\{H_1, H_2,H_3\cdots\}$ with interactions of range $\leq 2$ (i.e. no further than nearest-neighbors). ...
95 views

### What is the most general form of Hamiltonian to which MERA ansatz can be applied?

As far as I understand one can only use MERA(Multiscale Entanglement Renormalization Ansatz) to find ground state for Hamiltonians of following form(with possible simplifications due to additional ...
1k views

### What is the 'Drude Weight' and why is it important?

I have been trying to understand the Drude Weight quantity that is used in the Metal-Insulator transition and Spin chain literature, and I have not been able to find any clear intuitive explanations ...
350 views

### What is the relation between the Holstein-Primakoff Transformation and Bethe's Ansatz for the Heisenberg Ferromagnet?

Bethe's Ansatz is a method to find the eigenenergies and eigenstates of the Heisenberg ferromagnet (see also spin waves). For a general n-excitation state it involves solving rather complicated ...
2k views

### Detailed derivation and explanation of the AKLT Hamiltonian

I am trying to read the original paper for the AKLT model, Rigorous results on valence-bond ground states in antiferromagnets. I Affleck, T Kennedy, RH Lieb and H Tasaki. Phys. Rev. Lett. 59, 799 (...
401 views

302 views

### Differentiating between Tensor Networks

I am trying to study tensor networks and their application to quantum phase transitions. However, I had a question concerning the connection between the projected entangled-pair states (PEPS) and the ...
293 views

### Energy gap in Parent hamiltonian of MPS

Given a block injective matrix product state (MPS) with D blocks, how does the energy gap of corresponding parent hamiltonian scale with D? And is there a good reference which gives an analysis of ...
195 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 ...
2k views

### Confusion about duality transformation in 1+1D Ising model in a transverse field

In 1+1D Ising model with a transverse field defined by the Hamiltonian \begin{equation} H(J,h)=-J\sum_i\sigma^z_i\sigma_{i+1}^z-h\sum_i\sigma_i^x \end{equation} There is a duality transformation which ...
173 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 ...
527 views

### Naive questions on Goldstone modes and a possible duality relation?

For example, let's consider a 1D spin-1/2 ferromagnetic (FM) Heisenberg chain $H=-J\sum_{i=1}^{N}\mathbf{S}_i\cdot\mathbf{S}_{i+1}$ with periodic boundary conditions. Now we want to study its low ...
530 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 ...
1k views

### Interpretation of the 1D transverve field Ising model vacuum state in a spin-language

The 1D transverse field Ising model, \begin{equation} H=-J\sum_{i}\sigma_i^z\sigma_{i+1}^z-h\sum_{i}\sigma^x_i, \end{equation} can be solved via the Jordan-Wigner (JW) transformation (for further ...
2k views

### Simularity transformation of Heisenberg XXZ Hamiltonian

I am considering the Heisenberg XXZ Hamiltonian: $$H(\Delta, J) = J\sum_{i=1}^L\left(\sigma^x_i\sigma^x_{i+1} + \sigma^y_i\sigma^y_{i+1} + \Delta \sigma^z_i\sigma^z_{i+1} \right)$$ Apparently, one ...
132 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 ...
932 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. ...
608 views

### Undefined amplitudes in the Coordinate Bethe Ansatz for the XXX model?

Rather specific question for someone familiar with the Coordinate Bethe Ansatz... I am considering the Heisenberg XXX-model, consisting of a one-dimensional chain of L sites with a spin-1/2 particle ...
374 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?
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### 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 ...
4k views

### Prove that negative absolute temperatures are actually hotter than positive absolute temperatures

Could someone provide me with a mathematical proof of why, a system with an absolute negative Kelvin temperature (such that of a spin system) is hotter than any system with a positive temperature (in ...
2k views

### What is a free fermion model?

Title says it all really.. Why is the XX spin chain a free fermion (non-interacting) model, and the XXZ chain not? Is it right that $\sum_l a_l^\dagger a_{l+1}$ isn't an interaction between fermions ...
352 views

### Seeking a specific quantum spin system of interacting spin 1/2 particles

Is there a system of interacting quantum spin 1/2 particles (of any topology) whose the states where all spins are up or down are eigenstates of its Hamiltonian and yet does not conserve the total ...
416 views

### Have the correlation functions of the XY spin chain model been calculated using a functional partition function with source terms?

Have the correlation functions of the XY spin chain model, \begin{equation} H=-\sum_l (J_x \sigma_l^x \sigma_{l+1}^x+J_x \sigma_l^y \sigma_{l+1}^y)-B\sum_l \sigma_l^z \end{equation} been calculated ...