scholarly journals Displacement Transformations as a Tool to Study Many-Body Localization

2021 ◽  
Vol 9 ◽  
Author(s):  
Pablo Serna ◽  
Miguel Ortuño ◽  
Andrés M. Somoza
Keyword(s):  
Excited States ◽  
Short Range ◽  
The State ◽  
Large System ◽  
Many Body ◽  
Inverse Participation Ratio ◽  
One Dimensional ◽  
Participation Ratio

We obtain eigenstates of interacting disorder Hamiltonians using unitary displacement transformations that rotate the state of the system. The method generates excited states if the strength of these transformations is chosen to optimize the energy, while decreasing the energy variance. We apply the method to analyse the localization properties of one-dimensional spinless fermions with short range interactions, reaching relatively large system sizes. We quantify the degree of localization through the size and disorder dependence of the inverse participation ratio.

scholarly journals How many particles make up a chaotic many-body quantum system?

2021 ◽  
Vol 10 (4) ◽  
Author(s):  
Guy Zisling ◽  
Lea Santos ◽  
Yevgeny Bar Lev
Keyword(s):  
Long Range ◽  
Quantum Chaos ◽  
Short Range ◽  
Many Body ◽  
Interacting Particles ◽  
One Dimensional ◽  
Long Range Interactions ◽  
Minimum Number ◽  
Many Particles ◽  
Number Of Particles

We numerically investigate the minimum number of interacting particles, which is required for the onset of strong chaos in quantum systems on a one-dimensional lattice with short-range and long-range interactions. We consider multiple system sizes which are at least three times larger than the number of particles and find that robust signatures of quantum chaos emerge for as few as 4 particles in the case of short-range interactions and as few as 3 particles for long-range interactions, and without any apparent dependence on the size of the system.

scholarly journals Undecidability in quantum thermalization

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Naoto Shiraishi ◽  
Keiji Matsumoto
Keyword(s):  
Turing Machine ◽  
Thermal Equilibrium ◽  
General Theorem ◽  
Nearest Neighbour ◽  
Many Body ◽  
Initial State ◽  
One Dimensional ◽  
Universal Turing Machine ◽  
Many Body Systems ◽  
Neighbour Interaction

AbstractThe investigation of thermalization in isolated quantum many-body systems has a long history, dating back to the time of developing statistical mechanics. Most quantum many-body systems in nature are considered to thermalize, while some never achieve thermal equilibrium. The central problem is to clarify whether a given system thermalizes, which has been addressed previously, but not resolved. Here, we show that this problem is undecidable. The resulting undecidability even applies when the system is restricted to one-dimensional shift-invariant systems with nearest-neighbour interaction, and the initial state is a fixed product state. We construct a family of Hamiltonians encoding dynamics of a reversible universal Turing machine, where the fate of a relaxation process changes considerably depending on whether the Turing machine halts. Our result indicates that there is no general theorem, algorithm, or systematic procedure determining the presence or absence of thermalization in any given Hamiltonian.

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