Jeanne Colbois PRO
Physicist @ CNRS. Here you find slides for *some* of my presentations, as well as visual abstracts for recent publications.
LPT Toulouse - FFC Journal Club | 09.01.2023 | J. Colbois
arXiv:2211.13089 (v1)
Motivation / promise
1
- Large systems
- Any energy / eigenfunctions
Need
Idea
Promise
M
+ Combine efficiently
\(10^9\) non-interacting
\(10^6\) Two interacting particles
Time evolution
arXiv:2211.13089 (v1)
Plan
- Models
- Observables
- Algorithm(s)
- Some results
2
arXiv:2211.13089 (v1)
Models
3
arXiv:2211.13089 (v1)
(1) Mostly: \(t_{i, i+1} = t = 1\), \(\epsilon_i \) :
Irrational \(\beta\)
(2) Also:
\(\epsilon_i\) constant
Models
3
arXiv:2211.13089 (v1)
(1) Mostly: \(t_{i, i+1} = t = 1\), \(\epsilon_i \) :
Irrational \(\beta\)
(2) Also:
\(\epsilon_i\) constant
More delocalized
- locally clean
- translation invariance partially restored
Chiral (particle-hole) symmetry:
Delocalized region
Models : TIP
4
arXiv:2211.13089 (v1)
Only at strong disorder
Measurements
5
arXiv:2211.13089 (v1)
Density of states
Localization length
Participation ratio
D J Thouless 1972 J. Phys. C: Solid State Phys. 5 77
Algorithm(s)
arXiv:2211.13089 (v1)
General idea
H = H^S + H^{\mathrm{Env}}
H^S
- Partition and solve \(H_s\)
- Embed
- Eliminate
- (Time-evolve)
6
arXiv:2211.13089 (v1)
General idea
H = H^S + H^{\mathrm{Env}}
H^S
- Partition and solve \(H_s\)
- Embed
- Eliminate
- (Time-evolve)
Parallelization
6
arXiv:2211.13089 (v1)
1. Partitions: \(M\) sites
A_i = ] i, i+M] ,\quad i \in ]0, L-M]
7
arXiv:2211.13089 (v1)
i \in [0, L-M]
1. Partitions: \(M\) sites
A_i = ] i, i+M] ,\quad i \in ]0, L-M]
7
arXiv:2211.13089 (v1)
i \in [0, L-M]
1. Partitions: \(M\) sites
A_i = ] i, i+M] ,\quad i \in ]0, L-M]
7
arXiv:2211.13089 (v1)
i \in [0, L-M]
1. Partitions: \(M\) sites
A_i = ] i, i+M] ,\quad i \in ]0, L-M]
Repetitions
\(L-M\) sub-systems
7
arXiv:2211.13089 (v1)
i \in [0, L-M]
1. Partitions: \(M\) sites
A_i = ] i, i+M] ,\quad i \in ]0, L-M]
Repetitions
\(L-M\) sub-systems
7
arXiv:2211.13089 (v1)
i \in [0, L-M]
B_i = ]i \times \frac{M}{2}, i\times \frac{M}{2}+M] ,\quad 0 \leq i \leq \left \lceil \frac{2L}{M} \right \rceil
0 \leq i < \left \lfloor \frac{2L}{M} \right \rfloor
1. Partitions: \(M\) sites
A_i = ] i, i+M] ,\quad i \in ]0, L-M]
Repetitions
\(L-M\) sub-systems
B_i = ]i \times \frac{M}{2}, i\times \frac{M}{2}+M] ,\quad 0 \leq i \leq \left \lceil \frac{2L}{M} \right \rceil
7
arXiv:2211.13089 (v1)
0 \leq i < \left \lfloor \frac{2L}{M} \right \rfloor
i \in [0, L-M]
1. Partitions: \(M\) sites
A_i = ] i, i+M] ,\quad i \in ]0, L-M]
Repetitions
\(L-M\) sub-systems
B_i = ]i \times \frac{M}{2}, i\times \frac{M}{2}+M] ,\quad 0 \leq i \leq \left \lceil \frac{2L}{M} \right \rceil
7
arXiv:2211.13089 (v1)
0 \leq i < \left \lfloor \frac{2L}{M} \right \rfloor
i \in [0, L-M]
1. Partitions: \(M\) sites
A_i = ] i, i+M] ,\quad i \in ]0, L-M]
Repetitions
\(L-M\) sub-systems
B_i = ]i \times \frac{M}{2}, i\times \frac{M}{2}+M] ,\quad 0 \leq i \leq \left \lceil \frac{2L}{M} \right \rceil
7
arXiv:2211.13089 (v1)
0 \leq i < \left \lfloor \frac{2L}{M} \right \rfloor
i \in [0, L-M]
1. Partitions: \(M\) sites
A_i = ] i, i+M] ,\quad i \in ]0, L-M]
Repetitions
\(L-M\) sub-systems
B_i = ]i \times \frac{M}{2}, i\times \frac{M}{2}+M] ,\quad 0 \leq i \leq \left \lceil \frac{2L}{M} \right \rceil
7
arXiv:2211.13089 (v1)
0 \leq i < \left \lfloor \frac{2L}{M} \right \rfloor
i \in [0, L-M]
1. Partitions: \(M\) sites
A_i = ] i, i+M] ,\quad i \in ]0, L-M]
Repetitions
\(L-M\) sub-systems
B_i = ]i \times \frac{M}{2}, i\times \frac{M}{2}+M] ,\quad 0 \leq i \leq \left \lceil \frac{2L}{M} \right \rceil
7
arXiv:2211.13089 (v1)
0 \leq i < \left \lfloor \frac{2L}{M} \right \rfloor
i \in [0, L-M]
1. Partitions: \(M\) sites
A_i = ] i, i+M] ,\quad i \in ]0, L-M]
Repetitions
\(L-M\) sub-systems
B_i = ]i \times \frac{M}{2}, i\times \frac{M}{2}+M] ,\quad 0 \leq i \leq \left \lceil \frac{2L}{M} \right \rceil
7
arXiv:2211.13089 (v1)
0 \leq i < \left \lfloor \frac{2L}{M} \right \rfloor
i \in [0, L-M]
1. Partitions: \(M\) sites
A_i = ] i, i+M] ,\quad i \in ]0, L-M]
Repetitions
\(L-M\) sub-systems
B_i = ]i \times \frac{M}{2}, i\times \frac{M}{2}+M] ,\quad 0 \leq i \leq \left \lceil \frac{2L}{M} \right \rceil
7
arXiv:2211.13089 (v1)
\(\left \lceil \frac{2L}{M}\right\rceil \) sub-systems
Far less repetitions
\(M \) twice as large
0 \leq i < \left \lfloor \frac{2L}{M} \right \rfloor
i \in [0, L-M]
1. Partitions: \(M\) sites
x_1
\rho_1 = \frac{1}{N} \sum_{\alpha} |\tilde{\Phi}_{\alpha} \rangle \langle \tilde{\Phi}_\alpha|
\langle x_1 | N \rho_1 | x_1 \rangle < 1
A_i = ] i, i+M] ,\quad i \in ]0, L-M]
Repetitions
\(L-M\) sub-systems
B_i = ]i \times \frac{M}{2}, i\times \frac{M}{2}+M] ,\quad 0 \leq i \leq \left \lceil \frac{2L}{M} \right \rceil
7
arXiv:2211.13089 (v1)
\(\left \lceil \frac{2L}{M}\right\rceil \) sub-systems
Far less repetitions
\(M \) twice as large
0 \leq i < \left \lfloor \frac{2L}{M} \right \rfloor
i \in [0, L-M]
1. Partitions: \(M\) sites
x_1
\rho_1 = \frac{1}{N} \sum_{\alpha} |\tilde{\Phi}_{\alpha} \rangle \langle \tilde{\Phi}_\alpha|
\langle x_1 | N \rho_1 | x_1 \rangle < 1
A_i = ] i, i+M] ,\quad i \in ]0, L-M]
Repetitions
\(L-M\) sub-systems
B_i = ]i \times \frac{M}{2}, i\times \frac{M}{2}+M] ,\quad 0 \leq i \leq \left \lceil \frac{2L}{M} \right \rceil
7
arXiv:2211.13089 (v1)
\(\left \lceil \frac{2L}{M}\right\rceil \) sub-systems
Far less repetitions
\(M \) twice as large
0 \leq i < \left \lfloor \frac{2L}{M} \right \rfloor
i \in [0, L-M]
1. Partitions: \(M\) sites
x_1
\rho_1 = \frac{1}{N} \sum_{\alpha} |\tilde{\Phi}_{\alpha} \rangle \langle \tilde{\Phi}_\alpha|
\langle x_1 | N \rho_1 | x_1 \rangle = 1
A_i = ] i, i+M] ,\quad i \in ]0, L-M]
Repetitions
\(L-M\) sub-systems
B_i = ]i \times \frac{M}{2}, i\times \frac{M}{2}+M] ,\quad 0 \leq i \leq \left \lceil \frac{2L}{M} \right \rceil
7
arXiv:2211.13089 (v1)
\(\left \lceil \frac{2L}{M}\right\rceil \) sub-systems
Far less repetitions
\(M \) twice as large
0 \leq i < \left \lfloor \frac{2L}{M} \right \rfloor
i \in [0, L-M]
1. Partitions: \(M\) sites
x_1
x_2
\rho_1 = \frac{1}{N} \sum_{\alpha} |\tilde{\Phi}_{\alpha} \rangle \langle \tilde{\Phi}_\alpha|
\langle x_1 | N \rho_1 | x_1 \rangle = 1
\langle x_2 | N \rho_1 | x_2 \rangle < 1
A_i = ] i, i+M] ,\quad i \in ]0, L-M]
Repetitions
\(L-M\) sub-systems
B_i = ]i \times \frac{M}{2}, i\times \frac{M}{2}+M] ,\quad 0 \leq i \leq \left \lceil \frac{2L}{M} \right \rceil
7
arXiv:2211.13089 (v1)
\(\left \lceil \frac{2L}{M}\right\rceil \) sub-systems
Far less repetitions
\(M \) twice as large
0 \leq i < \left \lfloor \frac{2L}{M} \right \rfloor
i \in [0, L-M]
1. Partitions: \(M\) sites
x_1
x_2
\rho_1 = \frac{1}{N} \sum_{\alpha} |\tilde{\Phi}_{\alpha} \rangle \langle \tilde{\Phi}_\alpha|
\langle x_1 | N \rho_1 | x_1 \rangle = 1
\langle x_2 | N \rho_1 | x_2 \rangle < 1
A_i = ] i, i+M] ,\quad i \in ]0, L-M]
Repetitions
\(L-M\) sub-systems
B_i = ]i \times \frac{M}{2}, i\times \frac{M}{2}+M] ,\quad 0 \leq i \leq \left \lceil \frac{2L}{M} \right \rceil
7
arXiv:2211.13089 (v1)
\(\left \lceil \frac{2L}{M}\right\rceil \) sub-systems
Far less repetitions
\(M \) twice as large
0 \leq i < \left \lfloor \frac{2L}{M} \right \rfloor
i \in [0, L-M]
2. Embed
8
arXiv:2211.13089 (v1)
H = H^S + H^{\mathrm{Env}}
Real
Spurious
\(B_{i-1}\)
\ln(\tilde{\Phi}(x))
2. Embed
8
arXiv:2211.13089 (v1)
H = H^S + H^{\mathrm{Env}}
\(|\Phi\rangle\) localized in \(S\) :
Variance w.r.t environment
\(|\Phi\rangle\) eigenvector of \( H^S\):
\sigma_{\Phi}^2(H) = ||H^{\mathrm{Env}}|\Phi\rangle||^2
3. COMBINE / ELIMINATE
9
arXiv:2211.13089 (v1)
Alternative : Gram-Schmidt
Two steps:
No arbitrary cut-off
Much slower
1. \( |E_{\Phi} - E_{\Phi_k}| > \mathrm{num. }\, \mathrm{err} \quad \forall \, k \in \mathrm{rel.}\, \mathrm{clusters} \)
2. \( \langle \Phi_{j} | \Phi \rangle < \theta \) for all relevant \(k\)
\( \Rightarrow | \Phi \rangle \) is a new eigenfunction
Setting \(\theta\) :
\rho_1 = \frac{1}{N} \sum_{\alpha} |\tilde{\Phi}_{\alpha} \rangle \langle \tilde{\Phi}_\alpha|
Pop. on each site should not be larger than 1.
3. COMBINE / ELIMINATE
9
arXiv:2211.13089 (v1)
Two steps:
1. \( |E_{\Phi} - E_{\Phi_k}| > \mathrm{num. }\, \mathrm{err} \quad \forall \, k \in \mathrm{rel.}\, \mathrm{clusters} \)
2. \( \langle \Phi_{j} | \Phi \rangle < \theta \) for all relevant \(k\)
\( \Rightarrow | \Phi \rangle \) is a new eigenfunction
Setting \(\theta\) :
\rho_1 = \frac{1}{N} \sum_{\alpha} |\tilde{\Phi}_{\alpha} \rangle \langle \tilde{\Phi}_\alpha|
Pop. on each site should not be larger than 1.
- Before storing
- Previous overlapping subsystems
Parallelization:
4. Time evolution
10
arXiv:2211.13089 (v1)
|\psi_0\rangle = \sum_{\mu} |\Phi_{\mu} \rangle \langle \Phi_{\mu} | \psi_0\rangle
Prec. \(\epsilon\) on \(\langle\hat{O}\rangle\) \(\Rightarrow\)
# Eigenfunctions:
Accuracy of eigenfunctions:
\langle \Phi_{\mu} | \psi_0\rangle < \delta
Valid eigenfunctions : variance smaller than \(\delta^2\)
(Err. \(\delta\) in amplitude)
Single particle specificities
11
arXiv:2211.13089 (v1)
- \(L\) eigenfunctions
- Orthogonality : \(\mathrm{Tr}(\rho_1)\) = 1
- If missing: sites s.t. \(\langle x | N \rho_1| x \rangle < 1 \)
Termination criteria
Variance
\( S = [\alpha, \Omega]\)
TIP specificities (1)
12
arXiv:2211.13089 (v1)
Idea
- \(L \times (L-1) /2 \) eigenfunctions
- Most pairs unaffected
- Focus on subsystems of size M
BASIS
- \( M \times (M-1) /2\), but sparse
- Bandwidth \(M\) in \(\{|1,2\rangle, \dots , |1,M \rangle, |2,3 \rangle , \dots, |M-1, M \rangle\}\)
- Can be made \(M/2\) [Reverse Cuthill-McKee]
TIP specificities (2)
13
arXiv:2211.13089 (v1)
Variance
Termination criterion
Here \(|\Phi_{i}| ^2 = \sum_{j} |\langle i,j |\Phi\rangle |^2 \)
Smaller than a given cut-off.
Increase \(M\): new eigenstates, but independent of the value of the interaction
Algorithm Summary
arXiv:2211.13089 (v1)
Parameters
\(\sigma\)
\(\theta, \, \delta (\epsilon)\)
Simulation settings
14
\(M_{\mathrm{Max}} = 26000 \)
\(\Rightarrow V_{\mathrm{Min}} = 0.05 \): \(W^{\mathrm{box}}_{\mathrm{And.}} \sim 0.77\); \(W^{\mathrm{Gauss.}}_{\mathrm{And.}} = W^{\mathrm{Bin.}}_{\mathrm{And.}} \sim 0.44\)
Single particle
INteracting particles
Variance:
\sigma_0^2 = \begin{cases}
10^{-32} & \text{ strong disorder}\\
10^{-16} & \text{ weak disorder}
\end{cases}
Time evolution:
\(M_{\mathrm{Max}} = 200 \)
Variance:
\sigma_0^2 = 10^{-16}
\epsilon = \begin{cases}
10^{-3} & \text{ strong disorder}\\
10^{-1} & \text{ weak disorder}
\end{cases}
Overlap:
\(\theta = 10^{-5}\)
Overlap:
\(\theta = 10^{-7}\)
Time evolution:
\epsilon = \begin{cases}
10^{-5} & \text{ strong disorder}\\
10^{-2} & \text{ weak disorder}
\end{cases}
Performance
15
\(M \propto \xi \)
Assume
- \(M\) being \(L \)-independent
- \(M\) large enough
Limitations:
\mathcal{O}(\frac{L}{M} \times F(M)) = \begin{cases} \mathcal{O}(L \times M^2) & \text{ generic } \\
\mathcal{O}(L \times M) & \text{ tridiagonal }
\end{cases}
\(\xi \sim L\) (ergodic) \(\rightarrow\) usual complexity
\(\xi \ll L\) \(\rightarrow\) Dep. \(L\) : locally larger \(M\)
arXiv:2211.13089 (v1)
Performance
16
4 cores Inter Core i7-7700 CPU
- Box distribution
- \(M = 1000,500, 250\)
arXiv:2211.13089 (v1)
Performance
17
\(M\)
- Saturation : binary potential
- Aubry-André : delocalized eigenstates
Potential variance
arXiv:2211.13089 (v1)
S. Aubry and G. André, Ann. Israel Phys. Soc 3, 18, (1980)
Results
Strong
Weak
Single Particle
Two Interacting Particles
Eigenfunctions / Dynamics
Disorder
Properties of eigenfunctions
Strong disorder - single particle
18
\(10^9\) sites, Box distribution
\(W_{\mathrm{And.}} = 10\)
\(W_{\mathrm{MBL}} = 2.5\)
\(W_{\mathrm{And.}} = 20\)
\(W_{\mathrm{MBL}} = 5\)
\(W_{\mathrm{And.}} = 40\)
\(W_{\mathrm{MBL}} = 10\)
arXiv:2211.13089 (v1)
Strong disorder - TIP
19
Diff.
\(U = 0\)
\(U = 2\)
\(L = 10^5, W_{\mathrm{And.}} = 10\)
Box distribution
arXiv:2211.13089 (v1)
Strong disorder - TIP
20
\( U = 10, L = 10^6, W_{\mathrm{And.}} = 40\)
arXiv:2211.13089 (v1)
Strong disorder - TIP
20
\( U = 10, L = 10^6, W_{\mathrm{And.}} = 40\)
arXiv:2211.13089 (v1)
Weak disorder - Single particle
21
D.O.S., \(V = 0.05\), i.e. \(W_{\mathrm{Box, MBL}} = \) ; \(L = 10^8\) sites
arXiv:2211.13089 (v1)
Cusp : M. Kappus and F. Wegner,
Zeit. Phys. B 45,15–21 (1981)
Weak disorder - Single particle
22
Localization length, \(V = 0.05\), i.e. \(W_{\mathrm{Box, MBL}} = \) ; \(L = 10^8\) sites
arXiv:2211.13089 (v1)
G. Czycholl, B. Kramer, and A. MacKinnon, Zeit. Phys. B 43, 5–11 (1981)
M. Kappus and F. Wegner, Zeit. Phys. B 45,15–21 (1981)
B. Kramer and A. MacKinnon, Rep. Prog. Phys. 56, 1469 (1993)
Weak disorder - Single particle
23
Localization length, \(L = 10^8\) sites
arXiv:2211.13089 (v1)
G. Czycholl, B. Kramer, and A. MacKinnon, Zeit. Phys. B 43, 5–11 (1981)
M. Kappus and F. Wegner, Zeit. Phys. B 45,15–21 (1981)
B. Kramer and A. MacKinnon, Rep. Prog. Phys. 56, 1469 (1993)
Weak disorder - Single particle
24
\(L = 10^8\), Box distribution, \(V = 0.05\)
arXiv:2211.13089 (v1)
Weak disorder - Single particle
24
\(L = 10^8\), Box distribution, \(V = 0.05\)
arXiv:2211.13089 (v1)
Weak disorder - Single particle
24
\(L = 10^8\), Box distribution, \(V = 0.05\)
arXiv:2211.13089 (v1)
Weak disorder - TIP
25
\(L = 10^6\), \(W_{\mathrm{And}} = 4\)
\(V = 4\)
\(L = 10^6\), \(W_{\mathrm{And}} = 6\)
\(V = 3\)
arXiv:2211.13089 (v1)
Weak disorder - TIP
25
\(L = 10^6\), \(W_{\mathrm{And}} = 4\)
\(V = 4\)
\(L = 10^6\), \(W_{\mathrm{And}} = 6\)
\(V = 3\)
arXiv:2211.13089 (v1)
Weak disorder - TIP
25
\(L = 10^6\), \(W_{\mathrm{And}} = 4\)
\(V = 4\)
\(L = 10^6\), \(W_{\mathrm{And}} = 6\)
\(V = 3\)
arXiv:2211.13089 (v1)
Weak disorder - TIP
26
\(L = 10^6\), \(W_{\mathrm{And}} = 6\)
\(V = 3\)
\(L = 10^6\), \(W_{\mathrm{And}} = 4\)
\(V = 4\)
arXiv:2211.13089 (v1)
Weak disorder - TIP
26
\(L = 10^6\), \(W_{\mathrm{And}} = 6\)
\(V = 3\)
\(L = 10^6\), \(W_{\mathrm{And}} = 4\)
\(V = 4\)
arXiv:2211.13089 (v1)
Weak disorder - TIP
26
\(L = 10^6\), \(W_{\mathrm{And}} = 6\)
\(V = 3\)
\(L = 10^6\), \(W_{\mathrm{And}} = 4\)
\(V = 4\)
arXiv:2211.13089 (v1)
Weak disorder - TIP
26
\(L = 10^6\), \(W_{\mathrm{And}} = 6\)
\(V = 3\)
\(L = 10^6\), \(W_{\mathrm{And}} = 4\)
\(V = 4\)
arXiv:2211.13089 (v1)
Localized VS extended
27
Aubry-André model
\(L = 10^8\) sites
\rho_1 = \frac{1}{N} \sum_{\alpha} |\tilde{\Phi}_{\alpha} \rangle \langle \tilde{\Phi}_\alpha|
x_1
x_2
S. Aubry and G. André, Ann. Israel Phys. Soc 3, 18, (1980)
arXiv:2211.13089 (v1)
Localized VS extended
28
Bond disorder
\(L = 10^8\) sites
arXiv:2211.13089 (v1)
\(M = 10^4, 99.8\%\) of eigenstates
\(\Delta t = 0.5\)
Divergence : L. Balents and M. P. A. Fisher, Phys. Rev. B 56, 12970 (1997)
Localized VS extended
28
Bond disorder
\(L = 10^8\) sites
arXiv:2211.13089 (v1)
\(M = 10^4, 99.8\%\) of eigenstates
\(\Delta t = 0.5\)
Divergence : L. Balents and M. P. A. Fisher, Phys. Rev. B 56, 12970 (1997)
Localized VS extended
28
Bond disorder
\(L = 10^8\) sites
arXiv:2211.13089 (v1)
\(M = 10^4, 99.8\%\) of eigenstates
\(\Delta t = 0.5\)
Divergence : L. Balents and M. P. A. Fisher, Phys. Rev. B 56, 12970 (1997)
Localized VS extended
28
Bond disorder
\(L = 10^8\) sites
arXiv:2211.13089 (v1)
\(M = 10^4, 99.8\%\) of eigenstates
\(\Delta t = 0.5\)
Divergence : L. Balents and M. P. A. Fisher, Phys. Rev. B 56, 12970 (1997)
BONUS : Dynamics
Evolution of localized wavefunctions
Strong disorder dynamics
29
Long-time limit
Strong disorder, \(L = 10^9\)
\(t \in [9.500, 10.500]\)
arXiv:2211.13089 (v1)
Strong disorder dynamics
29
Long-time limit
Strong disorder, \(L = 10^9\)
\(t \in [9.500, 10.500]\)
arXiv:2211.13089 (v1)
Strong disorder dynamics
29
Long-time limit
Strong disorder, \(L = 10^9\)
\(t \in [9.500, 10.500]\)
arXiv:2211.13089 (v1)
Strong disorder dynamics
29
Long-time limit
Strong disorder, \(L = 10^9\)
\(t \in [9.500, 10.500]\)
arXiv:2211.13089 (v1)
Effect of interactions on strong disorder dynamics
30
arXiv:2211.13089 (v1)
\(L= 10^6\)
Effect of interactions on strong disorder dynamics
30
arXiv:2211.13089 (v1)
\(L= 10^6\)
Effect of interactions on strong disorder dynamics
30
arXiv:2211.13089 (v1)
Long-time limit
\(L= 10^6\)
weak disorder dynamics
31
arXiv:2211.13089 (v1)
Weak disorder,
\(L = 10^8\)
Box, \(V = 0.05\)
weak disorder dynamics
31
arXiv:2211.13089 (v1)
Weak disorder,
\(L = 10^8\)
Box, \(V = 0.05\)
Effect of interactions on weak disorder dynamics
32
arXiv:2211.13089 (v1)
Effect of interactions on weak disorder dynamics
32
arXiv:2211.13089 (v1)
Effect of interactions on weak disorder dynamics
32
arXiv:2211.13089 (v1)
Summary
arXiv:2211.13089 (v1)
- Approach from localized
- Diagnose missing eigenfunctions
- Large system sizes
Journal Club DaC Algorithm
By Jeanne Colbois
Journal Club DaC Algorithm
A journal club presentation of a recent preprint by L. Hernandez-Mulà and A. Läuchli on an algorithm to study Anderson localization and a two-interacting particles problem up to very large system sizes with a controllable error.
