Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [spin-chains]

The tag has no usage guidance.

1
vote
1answer
53 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
votes
0answers
37 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 ...
1
vote
0answers
64 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+...
2
votes
1answer
77 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
votes
1answer
94 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 (...
2
votes
2answers
131 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
votes
0answers
74 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, ...
1
vote
1answer
33 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 ...
0
votes
1answer
48 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) ...
0
votes
1answer
42 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+...
0
votes
1answer
75 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 ...
1
vote
0answers
21 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
votes
1answer
122 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
vote
1answer
46 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
vote
1answer
72 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 ...
1
vote
1answer
70 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 ...
0
votes
0answers
62 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 ...
2
votes
0answers
46 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. ...
1
vote
0answers
127 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
votes
0answers
139 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
votes
1answer
193 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 ...
0
votes
0answers
28 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?
0
votes
0answers
31 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
votes
0answers
49 views

Algebraic Bethe Ansatz and $R$-matrices [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
votes
1answer
124 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 ...
0
votes
0answers
72 views

Goldstone mode in 1D Heisenberg ferromagnet (Piers Coleman's book)

I am trying to understand the effect of the Goldstone mode in 1D Heisenberg ferromagnet (in Piers Coleman's Introduction to Many-body physics page 75-76) I already know how to transform the 1D ...
0
votes
0answers
55 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 ...
1
vote
0answers
55 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.
0
votes
0answers
47 views

Is $a_{k}^{\dagger} a_{k}= -a_{-k}^{\dagger}a_{-k}?$

Let $a_{k}^{\dagger} (a_{k})$ be the Fourier transform of the creation (annihilation) fermionic operator $a_{i}^{\dagger}(a_{i})$: $$a_{k}^{\dagger} = \frac{1}{\sqrt{L}}\sum_{i}^{L-1}e^{-ikx_{i}}a_{i}...
2
votes
0answers
104 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 {$...
1
vote
0answers
58 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 ...
0
votes
0answers
54 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 ...
1
vote
1answer
136 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 ...
1
vote
1answer
214 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: $$H = -J \sum_{<ij>} \mathbf S_i \mathbf S_j,$$ ...
1
vote
0answers
66 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 ...
0
votes
1answer
102 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+...
3
votes
0answers
202 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?
1
vote
0answers
43 views

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,...
4
votes
2answers
176 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.
4
votes
0answers
119 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 ...
0
votes
1answer
159 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} ...
1
vote
1answer
108 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 ...
0
votes
1answer
652 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 ...
3
votes
0answers
34 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 ...
3
votes
0answers
40 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 ...
1
vote
0answers
31 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). ...
3
votes
0answers
86 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 ...
3
votes
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 ...
4
votes
0answers
334 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 ...
12
votes
1answer
1k 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 (...