One dimensional quantum systems which can either be multiple discrete spin particles or their continuum limit.
Questions tagged [spin-chains]
234 questions
43
votes
8 answers
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 the sense that if a negative-temperature system…
user7757
33
votes
2 answers
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 (1987).
However I am stuck at Eq. $(1)$:
we choose…
Cheng Guo
- 689
- 7
- 8
29
votes
2 answers
$\phi^4$ 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 \partial^\mu \phi + \frac{\alpha}{\beta^2}\cos \beta…
octonion
- 9,072
29
votes
2 answers
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 defines new Pauli operators $\mu^x_i$ and…
Mr. Gentleman
- 1,606
17
votes
2 answers
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 reference about the explicit form of the JW…
VanillaSpinIce
- 1,458
17
votes
1 answer
Understanding Periodic and Anti-periodic boundary condition for Jordan-Wigner transformation
In the study of spin chains with periodic boundary condition ($S_{N+1}=S_{1}$) when one applies Jordan-Wigner transformation to map the spin chain to spinless fermion chain, one needs to make sure in the mapping the periodic boundary condition for…
Galilean
- 1,098
- 8
- 23
13
votes
2 answers
What is meant exactly by "renormalization" in condensed matter physics, specifically in density matrix renormalization group (DMRG)?
I first encountered the concept of renormalization in the context of statistical physics. Here, the renormalization "group" is a set of transformations of the system such that the Hamiltonian $H(J,\beta)$ is mapped to the same Hamiltonian with…
user2723984
- 4,878
13
votes
0 answers
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 Hamiltonians, on general interaction graphs, or tree-graphs?
I'm interested in frustration-free Hamiltonians such as the XXX…
Niel de Beaudrap
- 4,619
12
votes
1 answer
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 model. More concretely, at $\Delta = 1$ it undergoes…
Ruben Verresen
- 9,713
11
votes
1 answer
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 question has 2 main parts:
Is there a dual…
Luboš Motl
- 182,599
11
votes
1 answer
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 assumptions about the statistical weights, such…
Anton Kapustin
- 336
11
votes
1 answer
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
$\sum_{i_1,i_2\ldots i_N=1}^dTr(A_{i_1}A_{i_2}\ldots A_{i_N})|i_1,i_2\ldots i_N\rangle$,
with…
anurag anshu
- 801
- 6
- 16
10
votes
1 answer
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 (DMRG) to simulate a 1D many-body system. Before…
Sana Ullah
- 861
- 5
- 19
10
votes
3 answers
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 \sigma_l^z \sigma_{l+R}^z \rangle = \langle…
Jordan
- 1,663
10
votes
3 answers
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 energy excitations via the following two…
Kai Li
- 3,794
- 23
- 36