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Nature of Many-Body Localization and Transitions by Density Matrix Renormaliztion Group and Exact Diagonalization Studies
Strongly Correlated Electrons · Submitted 28 Oct 2015
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Combining En-DMRG with exact diagonalization simulations, we demonstrate that the transition from the MBL phase to the delocalized ergodic phase is driven by rare events where the locally entangled spin pairs develop long-range power-law correlations.
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The abstract, sentence by sentence
A many-body localized (MBL) state is a new state of matter emerging in a disordered interacting system at high energy densities through a disorder driven dynamic phase transition. The nature of the phase transition and the evolution of the MBL phase near the transition are the focus of intense theoretical studies with open issues in the field. We develop an entanglement density matrix renormalization group (En-DMRG) algorithm to accurately target the entanglement patterns of highly excited states for MBL systems. By studying the one dimensional Heisenberg spin chain in a random field, we demonstrate the high accuracy of the method in obtaining statistical results of quantum states in the MBL phase. Based on large system simulations by En-DMRG for excited states, we demonstrate some interesting features in the entanglement entropy distribution function, which is characterized by two peaks; one at zero and another one at the quantized entropy $S=ln2$ with an exponential decay tail on the $S>ln2$ side. Combining En-DMRG with exact diagonalization simulations, we demonstrate that the transition from the MBL phase to the delocalized ergodic phase is driven by rare events where the locally entangled spin pairs develop long-range power-law correlations. The corresponding phase diagram contains an intermediate regime, which has power-law spin-z correlations resulting from contributions of the rare events. We discuss the physical picture for the numerical observations in the intermediate regime, where various distribution functions are distinctly different from results deep in the ergodic and MBL phases for finite-size systems. Our results may provide new insights for understanding the phase transition in such systems.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | A many-body localized (MBL) state is a new state of matter emerging in a disordered interacting system at high energy densities through a disorder driven dynamic phase transition. | background 1.00 | 0.06 | 0.04 | asserted 1.00 |
| s1 | The nature of the phase transition and the evolution of the MBL phase near the transition are the focus of intense theoretical studies with open issues in the field. | background 0.62 | 0.04 | 0.02 | asserted 0.98 |
| s2 | We develop an entanglement density matrix renormalization group (En-DMRG) algorithm to accurately target the entanglement patterns of highly excited states for MBL systems. | method 0.79 | 0.97 | 0.04 | asserted 1.00 |
| s3 | By studying the one dimensional Heisenberg spin chain in a random field, we demonstrate the high accuracy of the method in obtaining statistical results of quantum states in the MBL phase. | method 0.42 | 0.95 | 0.04 | asserted 1.00 |
| s4 | Based on large system simulations by En-DMRG for excited states, we demonstrate some interesting features in the entanglement entropy distribution function, which is characterized by two peaks; one at zero and another one at the quantized entropy $S=ln2$ with an exponential decay tail on the $S>ln2$ side. | result 1.00 | 0.97 | 0.14 | asserted 1.00 |
| s5 | Combining En-DMRG with exact diagonalization simulations, we demonstrate that the transition from the MBL phase to the delocalized ergodic phase is driven by rare events where the locally entangled spin pairs develop long-range power-law correlations. | result 0.89 | 0.96 | 0.62 | asserted 1.00 |
| s6 | The corresponding phase diagram contains an intermediate regime, which has power-law spin-z correlations resulting from contributions of the rare events. | result 0.97 | 0.85 | 0.15 | asserted 1.00 |
| s7 | We discuss the physical picture for the numerical observations in the intermediate regime, where various distribution functions are distinctly different from results deep in the ergodic and MBL phases for finite-size systems. | interpretation 0.93 | 0.74 | 0.07 | asserted 0.81 |
| s8 | Our results may provide new insights for understanding the phase transition in such systems. | interpretation 0.91 | 0.30 | 0.07 | hedged possibility 1.00 |
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The paper
Original abstract
A many-body localized (MBL) state is a new state of matter emerging in a disordered interacting system at high energy densities through a disorder driven dynamic phase transition. The nature of the phase transition and the evolution of the MBL phase near the transition are the focus of intense theoretical studies with open issues in the field. We develop an entanglement density matrix renormalization group (En-DMRG) algorithm to accurately target the entanglement patterns of highly excited states for MBL systems. By studying the one dimensional Heisenberg spin chain in a random field, we demonstrate the high accuracy of the method in obtaining statistical results of quantum states in the MBL phase. Based on large system simulations by En-DMRG for excited states, we demonstrate some interesting features in the entanglement entropy distribution function, which is characterized by two peaks; one at zero and another one at the quantized entropy $S=ln2$ with an exponential decay tail on the $S>ln2$ side. Combining En-DMRG with exact diagonalization simulations, we demonstrate that the transition from the MBL phase to the delocalized ergodic phase is driven by rare events where the locally entangled spin pairs develop long-range power-law correlations. The corresponding phase diagram contains an intermediate regime, which has power-law spin-z correlations resulting from contributions of the rare events. We discuss the physical picture for the numerical observations in the intermediate regime, where various distribution functions are distinctly different from results deep in the ergodic and MBL phases for finite-size systems. Our results may provide new insights for understanding the phase transition in such systems.
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How the literature uses it
8 arXiv papers cite this in 23 sentences
Papers citing it · 13 sentences without a confident label
Builds on it 1 paper
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Our results were obtained using long-term, large-scale numerics (up to bond dimensions of $χ∼1700$) and hence complement and extend the data presented in Refs. [ref] .
Entanglement scaling of excited states in large one-dimensional many-body localized systems · Raw data · 0.90
Compares with it 3 papers
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The regime close to the critical point, dominated by Griffiths effects, has also recently been studied using a matrix product state based method to access larger system sizes in Ref. [ref] together with exact diagonalization and the exponential tail of the distribution was also observed as well as a broad histogram[It should be noted that the differences in the details of the distributions in Ref. [ref] and the present work are due to different boundary conditions: Here we use periodic boundaries, while Ref. [ref] employ open boundary conditions.] at $h=3$.
Long tail distributions near the many body localization transition · Probability distributions of the entanglement entropy · 0.88
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For reasons of completeness, we finally show the probablity distribution $P(S)$ of the entanglement in Fig. [ref]; it exhibits a peak at $ln(2)$ in agreement with the results of Refs. [ref] .
Entanglement scaling of excited states in large one-dimensional many-body localized systems · Scaling of the entanglement; mobility edge · 0.84
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Of course, the CG scheme induces extra errors, but as we have shown they are not severe; for example, our obtained energy variance (Fig. [ref]) is comparable or lower than other approaches [ref] .
Power-Law Entanglement Spectrum in Many-Body Localized Phases · B.2 Performance of the algorithm and discussion · 0.97
Cites it as background 4 papers
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As mentioned above, similar studies (using more elaborate algorithms) appeared shortly before the completion of our paper [ref] .
Entanglement scaling of excited states in large one-dimensional many-body localized systems · Raw data · 0.86
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However, the probability distributions of the entanglement entropy have received less attention until recently [ref] , possibly due to the daunting requirement for the number of disorder realizations to obtain a satisfactory resolution of the histogram.
Long tail distributions near the many body localization transition · Probability distributions of the entanglement entropy · 0.93
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MBL has also stimulated considerable progress in developing tools for describing excited eigenstates of many-body systems [ref] .
Fixed points of Wegner-Wilson flows and many-body localization · Introduction · 0.82
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