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Questions tagged [spin-chains]

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Partial Transpose in Gapped Time-reversal Symmetric Spin Chains

Suppose you have a one-dimensional quantum spin system with on-site Hilbert spaces $\mathcal{S}$. Suppose there is an anti-unitary, anti-linear operator $C$ on $\mathcal{S}$ inducing an anti-linear, ...
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52 views

Physical Interpretation of the Spectrum of MPS Transfer Matrices

Take an injective, translation invariant MPS with transfer matrix $E = \sum_\sigma \overline{A^\sigma} \otimes A^\sigma$ (i am using the terminology of https://arxiv.org/abs/quant-ph/0410227 , eq. (6))...
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1answer
49 views

Bose-Einstein distribution and magnons

I have some doubt about the Bose-Einstein distribution for magnons/spin-waves. A one-dimensional ferromagnet placed in an external magnetic field $\mathbf{B} = B\, \hat{z}$ obeys the Hamiltonian $$H ...
4
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0answers
224 views

Absence of phase transitions in quantum 1D systems at positive temperature

While it is generally said that there are no phase transitions in classical lattice systems in one spatial dimension, there are also exceptions to this rule. Rigorous proofs involve some fairly strong ...
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1answer
41 views

Lieb-Robinson bound and spin chain

I am trying to understand the paper Localized shocks better. There is Lieb-Robinson bound on the page 6. How does formula (7) imply that: the radius of the operator can grow no faster than linearly ...
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0answers
13 views

Pinch points in fidelity per site (quantum phase transitions)

In Sachdev's Quantum Phase Transitions he defines a quantum phase transition in an infinite lattice as the point in which the ground energy as a function of the parameters of the system becomes non-...
0
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1answer
49 views

Spin-1 Heisenberg model, the AKLT model, and their ground states

I am reading literature on quantum spin chains and matrix product states, and I notice similar arguments regarding the spin-1 antiferromagnetic Heisenberg model, $H_{H} = \sum_i S_i \cdot S_{i+1}$, ...
2
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2answers
71 views

How can I simulate a ground state degenerate system numerically?

I'm using numerical method like DMRG to simulate ground state of correlated systems. But the degeneracy of the ground state has long bothered me: When degeneracy exists the ground state isn't unique. ...
1
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1answer
70 views

One-dimensional $SU(3)$ Heisenberg Model, the non-linear sigma model, $\theta$-term

Let's consider a one dimensional $SU(N)$ antiferromagnetic Heisenberg Model with an irreducible representation and its conjugate on alternating sites, such that they correspond to a Young tableaux ...
2
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0answers
44 views

How does the complexity in Matrix Product states ansatz drop from $D^N$ to $ND$?

I have just started to read about DMRG and MPS. It is said that in case of simple 1D chain with spins states $|\uparrow\rangle$; $|\downarrow\rangle$ and any state in the complete Hilbert space of ...
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0answers
72 views

How to find groundstate energy of a simple Hamiltonian at $N/L$-filling using Jordan-Wigner (JW) transformation?

$\underline{\textbf{Model:}}$ Let we have the $t-V$ model for spinless fermions on a 1D lattice, which is defined in second quantization operators as follows: $$H_1 = -t\sum_i \big(c_i^\dagger c_{i+...
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1answer
104 views

Why do we use matrix product states?

Given a many body $\vert\psi\rangle$, we can express it in terms of a matrix product state. That is, $\vert\psi\rangle = \sum_{i,j..k}\psi_{i,j..k}\vert i,j..k\rangle$ can be rewritten as $\vert\...
5
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1answer
115 views

Is there any relation between density matrix renormalization group (DMRG) and renormalization group (RG)?

Probably I am going to receive many down-votes for this post but I really need to ask this question here. I am new to statistical mechanics. I wanted to learn Density Matrix Renormalization Group (...
3
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2answers
177 views

How can I explicitly express the Ising Hamiltonian in matrix form?

I am reading this book about numerical methods in physics. It has the following question: Consider the Ising Hamiltonian defined as following $$H=-\sum_ {i=1}^{N-1} \sigma_i^x \sigma_ {i+1} ^x + h ...
3
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0answers
81 views

Resource recommendation: Tensor Networks

I want to learn tensor network methods for condensed matter systems. I went through some basic papers (i.e. 1,2) and come to know that there are many things (i.e. different math, tensors, ...
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1answer
39 views

Algebraic Bethe Ansatz state generator problem

Given $B(\lambda)=T^0_1 (\lambda)$ the component of the monodromy matrix T that creates a state, $\lambda$ the spectral parameter and $| \Omega \rangle$ the reference ground state, In "Quantum Groups ...
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1answer
60 views

One-dimensional Ising Model in a three spin chain

I have a system of three aligned spins with $S=\frac{1}{2}$. There are interactions between nearest neighbors, and each spin has a magnetic moment. The Hamiltonian of the system is: $$H=J[S_z(1)S_z(2) ...
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1answer
50 views

Average entropy of a subsystem

In this paper by Don Page, https://arxiv.org/pdf/gr-qc/9305007.pdf, He conjectures average entropy of a substem of dimension m with Hilbert space dimension mn, $m \leq n$. to be : $ S_{mn} = \sum_{n+...
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1answer
99 views

Hamiltonian for a 1D spin chain [closed]

I am trying to implement the Lanczos algorithm to tridiagonalize the Hamiltonian for a 1D spin chain of length $L$, but I am unable to decipher from my professor's notes (here's a link), what the ...
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0answers
25 views

Discrepancy regarding Husimi Probability distribution calculation

I am trying to simulate a system of j qubits and for visualization of the dynamics considering the Husimi distribution of the state. To carry out the projection onto coherent states I have proceeded ...
2
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1answer
130 views

Integrability of generalized Richardson-Hubbard model

Recently I got a bit interested in the possibility of finding spectrum of few interesting class of lattice quantum mechanical hamiltonians like Richardson's pairing hamiltonian, 1D Hubbard hamiltonian,...
1
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1answer
50 views

Reduced density matrix of the edge spin-1/2 in AKLT spin chain

I am trying to understand the paper titled, "Entanglement in a Valence-Bond-Solid State" by Fan, Korepin, and Roychowdhury (https://arxiv.org/abs/quant-ph/0406067). I was able to understand the ...
1
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1answer
116 views

Hamiltonian Matrix for XXZ Model

Given the XXZ model Hamiltonian, $H = -\frac{1}{2}\sum^{N}_{i}(\sigma_{i}^{x}\sigma_{i+1}^{x}+\sigma_{i}^{y}\sigma_{i+1}^{y}+\Delta\sigma_{i}^{z}\sigma_{i+1}^{z})$ The two-site Hamiltonian reads $H ...
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1answer
77 views

About spin chain string order

We know that the string order of a spin chain is defined as $$\mathcal{O}^\alpha=\lim_{i-j\to\infty}\left\langle S_i^\alpha\prod_{k=i+1}^{j-1}\exp(i\pi S_k^\alpha)\ S_j^\alpha \right\rangle$$ now ...
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0answers
63 views

Correlation length

I am working with the spin-1/2 quantum antiferromagnet Heisenberg model. I have found literature about the correlation length of this model for 2D. However, what would it be in 1D? I have the ...
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0answers
53 views

Can we have a spin glass in the one-dimensional Heisenberg hamiltonian with nearest neighbours only?

Consider the one dimensional Heisenberg Hamiltonian of the form \begin{equation} H = - \sum_{<i,j>} J_{ij} \mathbf{S}_i \cdot \mathbf{S}_j \end{equation} with nearest neighbour interactions. ...
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0answers
152 views

Transverse field Ising model with open boundary conditions

what is the energy dispersion of the transverse field Ising model looks like in the case of open boundary conditions? In the case of periodic boundary, the energy takes the form of and the ground ...
4
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0answers
174 views

Mermin-Wagner and Heisenberg spin chains

The Hamiltonian for the spin 1/2 ferromagnetic Heisenberg spin chain is $H=-J\sum_i \vec \sigma_i \cdot \vec\sigma_{i+1}$ with $J>0$ and $\vec\sigma_i$ the Pauli matrices acting on ith lattice site....
3
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1answer
222 views

R-matrix for spin chains

In algebraic Bethe ansatz procedure, one of the central objects is the R-matrix satisfying the Yang-Baxter equation, but all the papers/books give directly its expression without deriving it, so my ...
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31 views

Elliptic R-matrix and Yang Baxter solution for XYZ model [duplicate]

in the framework of QISM, How can i derive the R-matrix for XYZ Heisenberg model?
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34 views

$R$ matrix for XYZ spin chain [duplicate]

Trying to understand how the Algebraic Bethe Ansatz works, I'm actually reading some papers and trying to apply for XXZ or XYZ model. But my problem is that I don't know how to find the R-matrix ...
0
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1answer
148 views

Block diagonalizing a spin-chain Hamiltonian

$\newcommand{\ket}[1]{\left|#1\right>}$ I am learning about exact diagonalization methods, currently following this explanation. My question is in regards to the part where we utilize the fact ...
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61 views

Why is translation symmetry an important recipe in performing a Fourier transform?

In page 3 of Vodola's dissertation, Correlations and Quantum Dynamics of 1D Fermionic Models: New Results for the Kitaev Chain with Long-Range Pairing, it was stated that assuming translation symmetry ...
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0answers
61 views

Reference for Bethe Ansatz solution of 1D spinless Hubbard model

I want to numerically solve 1D spinless Hubbard model using Bethe Ansatz. Can you provide me some online references for that.
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0answers
119 views

The string hypothesis of the Bethe solutions of Heisenberg XXX model

I am studying L. Fadeev's "How Algebraic Bethe Ansatz works for integrable model". He takes Heisenberg $XXX_{1/2}$ model as an example. After obtaining the Bethe Ansatz Equations (BAE) for the roots {$...
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0answers
68 views

Boundary critical exponents of the 1D quantum XY model

Critical properties of the two-dimensional Ising model in the bulk and at the boundary are characterized by different critical exponent, see Ising model: exact results and McCoy: The boundary Ising ...
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58 views

References or resource recommendation for mapping of 1D spinless Hubbard model into XXZ Heisenberg model

I read from somewhere that 1D spinless Hubbard model can be mapped onto XXZ Heisenberg model but I don't remember from where did I read this sentence. I tried googling it but couldn't find any thing ...
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1answer
152 views

Does one-dimensional ferromagnetic chain have long range order at zero tempreture?

In many text books on one dimensional quantum magnetic systems, it's said there is no orderd state for one dimensional magnetic systems. I understand that the one dimensional spin half ...
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1answer
243 views

Heisenberg ferromagnet in continuum limit

I consider the case of the simple, say 2D, Heisenberg ferromagnet with exchange interaction between the nearest neighbors. The Hamiltonian is: $$H = -J \sum_{<ij>} \mathbf S_i \mathbf S_j,$$ ...
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0answers
67 views

How does one bound the growth of the support of local operators in the Transverse-Field Ising Chain?

Consider the transverse-field Ising chain (TFIC) in a transverse-field $B$: $$H_{TFIC}(B)\equiv -\sum_{j=1}^{N-1} \sigma^x_j\sigma^x_{j+1}+B\sum_{j=1}^N \sigma^z$$ At $B=0$, we have the classical ...
4
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1answer
124 views

Is there any qualitative difference between the WZW $SO(2)_1$ and the WZW $SU(2)_1$ CFT?

Consider the anisotropic spin-$\frac{1}{2}$ Heisenberg chain $$H = \sum_{n=1}^N S^x_n S^x_{n+1}+S^y_n S^y_{n+1} + \Delta S^z_n S^z_{n+1}$$ which for $\Delta = 0$ realizes the Wess-Zumino-Witten (WZW) $...
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1answer
108 views

ground state of spin chain with $Z_i X_{i+1} Z_{i+2}$ interaction

the problem comes from transverse field Ising model, with an extra 3-spin interaction term $$H=H_0+H_1+H_2=-h\sum_{i=1}^{N}X_i -\lambda_1 \sum_{i=1}^{N-1}Z_i Z_{i+1}-\lambda_2 \sum_{i=1}^{N-2}Z_i X_{i+...
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0answers
218 views

Density Matrix Renormalization Group (DMRG) and Bethe ansatz for 1D Hubbard model

Has Density Matrix Renormalization Group (DMRG) been benchmarked against the exact Bethe ansatz result for the one dimensional Hubbard chain? If yes, then what are the relevant references?
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Why is the ground energy of this spin-1 chain four-fold degenerate?

In this paper the author found that the ground state of the following Hamiltonian $$ H = \sum_{i=1}^{L-1} [S_i \cdot S_{i+1} - \beta (S_i \cdot S_{i+1 })^2] , $$ where $\beta $ is a real parameter,...
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2answers
189 views

Simple problem solvable with Bethe ansatz [closed]

I want some exercise for my students. Is there any simple but still non-trivial problem which can be solved with Bethe ansatz? The Heisenberg model is still too heavy.
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0answers
141 views

Kosterlitz-Thouless in the XXZ chain: instanton condensation?

The anisotropic spin-$\frac{1}{2}$ Heisenberg chain $$H = \sum_n S^x_n S^x_{n+1} + S^y_n S^y_{n+1} + \Delta S^z_n S^z_{n+1}$$ is known to have the same physics as the two-dimensional classical XY ...
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1answer
180 views

Matrix form of the 1D quantum Ising model mapped to free fermion model via the Jordan -Wigner Transformation

The free fermion Hamiltonian for the 1D quantum Ising model is $$H = -J\sum_i (c_{i}^{\dagger }c_{i+1} +c_{i+1}^{\dagger }c_{i}+c_{i}^{\dagger }c_{i+1}^{\dagger }+c_{i+1}c_{i}-2gc_{i}^{\dagger }c_{i} ...
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1answer
118 views

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
750 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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0answers
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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 ...