All Questions
Tagged with spin-chains condensed-matter
76
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What is the Haldane gap?
The Haldane Phase is a topological phase of matter in which a Haldane gap opens due to the breaking of either time-reversal symmetry or inversion symmetry. Physically speaking, what is the "...
- 43
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Why is the excitation energy of antiferro 1/2 spin XXZ chain associated with the $\psi_{n+2}$ and $\psi_{n-2}$
I do not understand the equation on page 5 of nagaoso's book "quantum field theory in strongly correlated electronic systems".
The Hamiltonian is shown in this form
$H=\frac{J_\bot}{2}\sum_{...
- 11
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62
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Relative Sign In XXZ Chain
This is a relatively simple question that I just want confirmation on. In literature, I have seen 2 ways of writing the Heisenberg XXZ Chain:
1.) $H = -J \sum_{n=1}^{N}\left(S_n^xS_{n+1}^x+ S_n^yS_{n+...
- 35
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Phase transitions in the XXZ model
Consider the one-dimensional quantum XXZ model defined by the Hamiltonian:
$$
H = J \sum_{i} \left (X_i X_{i+1} + Y_i Y_{i+1} + \Delta Z_i Z_{i+1} \right).
$$
First, let us focus at zero ...
- 31
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108
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Can the hybridization of edge states in the 1D SSH model be observed numerically?
So I was reading the lecture notes by Asboth on topological insulators . In the first chapter the SSH model is discussed :
$H_{SSH} = \sum_{i = 1}^N v|i,A\rangle \langle i,B | + h.c. + \sum_{i = 1}^{N-...
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2
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Ground state energy of infinite Heisenberg XXX model with open or periodic boundary conditions equal?
I was wondering if there is anywhere a formal proof that shows that the ground state energy of a Heisenberg XXX model with periodic boundary conditions becomes equal to the ground state energy with ...
- 98
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Calculate partition function of 1D quantum Heisenberg models?
For the 1D Quantum Heisenberg Spin Model:
$\displaystyle {\hat H = -\frac{1}{2} \sum_{j=1}^{N} (J_x \sigma_j^x \sigma_{j+1}^x + J_y \sigma_j^y \sigma_{j+1}^y + J_z \sigma_j^z \sigma_{j+1}^z + h\...
- 99
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77
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Exact ground state degeneracy for quantum spin system with non commuting terms and its quantum phase transition?
Let's say I have a 2D quantum spin model of N spin-1/2 particles, with two terms:
$$
H = -J \sum_N \prod_{i \in G} \sigma^x_i - h \sum_N \prod_{i \in G'} \sigma^z_i
$$
The first is a collection of ...
- 29
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132
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Is the dot product of spins the only way to create a scalar (Hamiltonian) invariant under spin rotation?
I wanted to generalize the result for the following question for four spins 1/2: Most general form of a spin rotation invariant Hamiltonian?.
Assume that we have a Hilbert space for four spins $(\vec{...
7
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576
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Most general form of a spin rotation invariant Hamiltonian?
I am told that the most general form of a spin rotation invariant Hamiltonian for two systems 1 and 2 both with spin $S$, i.e., the spin operators
\begin{align}
(\hat{S}_1^x)^2 +(\hat{S}_1^y)^2 + (\...
- 904
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0
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101
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iTEBD real time evolution for 3-body time evolution operator
I am trying to implement the iTEBD algorithm for real-time evolution of the PXP model. Here, $P$ is the projector onto the ground state, and $X$ is the Pauli spin matrices.
I know for the 2-body case, ...
- 193
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Why the ground-state energy of S-1/2 Anti-Ferromagnetic Heisenberg Chain is not$-\frac{N}{4}J$
The Hamiltonian of traditional Heisenberg model is
$$\hat H = J\sum_{<i,j>}\vec{S_i}\cdot\vec{S_j}=J\sum_{<i,j>}\left(S_i^zS_j^z+\frac{1}{2}\left(S_i^+S_j^-+S_i^-S_j^+\right)\right)$$
if J ...
- 53
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Writing the Random Matrix model corresponding to any physical hamitonian model
I am an amateur in Random Matrix Theory (RMT). In RMT, we start with ensemble of a random matrices of a certain symmetry classes (GOE, GUE..) to find the various distribution of our interest, e.g.- ...
- 244
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How does the proof for the area law for 1D systems work?
I am currently reading this paper in order to understand the proof of the area law for one dimensional, low energy systems such as 1D spin chains. The main area law theorem is given on page 13 and is ...
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How to stack two Haldane chains?
This questions is a follow up to a pervious question of mine:
Inverse of Haldane phase?
Now that I know that Haldane phase is it's own inverse, I am having trouble is visualizing how could we stack ...
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