All Questions
Tagged with spin-chains computational-physics
17
questions
1
vote
0
answers
43
views
Limit of solving the 1D Heisenberg chain to find the dynamics numerically
I am trying to simulate the dynamics of a 1D Heisenberg chain using Python.
I am going step-by-step.
There is an external magnetic field along +Z direction.
At first we consider a single classical ...
2
votes
0
answers
88
views
How non-local can the interactions be for Density Matrix Renormalization Group (DMRG) to still work?
I know that Density Matrix Renormalization Group (DMRG) / Tensor Networks (TN) work well for local Hamiltonians, where on each site I have a fermion or boson, which only have nearest-neighbor ...
- 2,921
-1
votes
1
answer
248
views
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
0
votes
1
answer
142
views
Question about the 'reduced basis transformation'
I' ve been reading the review Ulrich Schollwöck: The density-matrix renormalization group in the age of
matrix product states (arXiv link)
and encountered with a question about the so called 'reduced ...
- 133
2
votes
0
answers
133
views
Normalization in tensor networks [closed]
I am trying to implement the iTEBD algorithm for the $PXP$ model, i.e, the hamiltonian is
$$H = \sum_iP_{i-1}X_iP_{i+1}.$$
Here $P$ is the projector onto the ground state and $X$ is the usual pauli x ...
- 193
0
votes
1
answer
144
views
How do you calculate the entanglement entropy of a tensor network?
I found that the entanglement entropy can be calculated using the Schmidt coefficients of the state, using
$S = -\sum_i|\alpha_i|^2\log(|\alpha_i|^2)$
In the case of tensor networks, does this simply ...
- 193
3
votes
0
answers
144
views
Calculating entanglement negativity without constructing density matrix
There are two procedures that I know of for finding the von Neumann entanglement entropy of a bipartite system split between $A$ and $B$ - a bad way and a better way. I have in mind computationally ...
- 2,292
1
vote
1
answer
311
views
Can bond dimension vary from bond to bond?
Consider a bipartite system composed of subsystems $A$ and $B$, with corresponding Hilbert spaces $\mathcal{H}_A$ and $\mathcal{H}_B$, spanned by $\{\chi_1,...,\chi_n\}$ and $\{\phi_1,...,\phi_m\}$, ...
- 327
0
votes
1
answer
183
views
Truncation Problem of Density Matrix Renormalisation Group (DMRG)
I am wondering that is there any restrictions for the truncation in DMRG algorithm. Currently I am using DMRG to calculate ground state energy per site of a many-body system described by on-site ...
- 413
1
vote
1
answer
955
views
Matrix product state (MPS): Creating and understanding a specific 2-site Ising ground state?
I've been trying to better understand matrix product states (in order to implement them in code in the near future), so I'm considering small examples. I was wondering if I could get some ...
- 419
0
votes
1
answer
177
views
Tensor Network/MPS Code examples for simple condensed matter systems?
I've been recently learning about numerical methods in physics, and have come across matrix product states and tensor networks. This is definitely a vague question, but I was wondering if anyone knew ...
- 419
13
votes
2
answers
1k
views
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,\...
- 4,736
4
votes
2
answers
763
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. ...
- 118
9
votes
1
answer
791
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 (...
- 831
3
votes
2
answers
2k
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 ...
- 1,335