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 ...
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1answer
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 ...
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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 ...
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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 ...
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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). ...
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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 ...
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2answers
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 ...
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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 ...
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1answer
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 (...
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1answer
401 views

Goldstone mode as spin wave in 2D?

I'm trying to understand how Goldstone modes destroy long range order in 1D and 2D spin lattice. I started with a spin chain, using 1D XY-model, which has continuous symmetry. $H=- \sum_{<i j>} ...
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1answer
220 views

Zero modes $a_j\sim e^{-\kappa j}$ in a semi-infinite quantum Ising chain?

As a way of analyzing the performance of quantum annealing, I've been studying quantum diffusion in fermionizable lattice models with zero modes. In particular, the 1+1D quantum Ising model, semi-...
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132 views

Localization length in Anderson localized systems

In Anderson localized systems, a great portion of the system's properties are governed by the localization length. These phenomena are well understood and have been studied for ages. However, I could ...
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2answers
722 views

Simple analytic examples of Multi-scale Entanglement Renormalization Ansatz (MERA)

I want to understand Multi-scale Entanglement Renormalization Ansatz (MERA) with very elementary examples. So far I could find references which are mostly based on numerics. It would be a great help ...
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80 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 ...
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$\phi^4$ 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 \...
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88 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 ...
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103 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: ...
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80 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 \...
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1answer
658 views

Parent hamiltonian of AKLT state

Given a translationally invariant Matrix Product State (assuming periodic boundary condition) on $N$ sites of dimension $d$ each, which takes the form $\sum_{i_1,i_2\ldots i_N=1}^dTr(A_{i_1}A_{i_2}\...
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2answers
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 ...
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1answer
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 ...
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2answers
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 ...
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2answers
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 ...
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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 ...
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3answers
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 ...
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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 ...
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1answer
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 ...
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1answer
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 ...
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1answer
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 ...
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1answer
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. ...
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1answer
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 ...
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0answers
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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417 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 ...
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7answers
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 ...
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1answer
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 ...
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1answer
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 ...
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1answer
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 ...
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1answer
1k views

Dual conformal symmetry and spin networks in ABJM

In this question, I would love to hear some independent opinions on an issue I asked Juan Maldacena, Nathan Berkovits, Dan Jafferis, and others, but all the physicists may be missing something. The ...
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3answers
2k views

To calculate the correlation functions of an XX spin chain, Wick's theorem is used. But is it valid for a chain of any size?

The correlation functions found in Barouch and McCoy's paper (PRA 3, 2137 (1971)) for the XX spin chain use a method which uses Wick's theorem. For the zz correlation function, this gives $\langle \...