scholarly journals Fermionic criticality is shaped by Fermi surface topology: a case study of the Tomonaga-Luttinger liquid

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Anirban Mukherjee ◽  
Siddhartha Patra ◽  
Siddhartha Lal
Keyword(s):  
Fermi Surface ◽  
Critical Point ◽  
Entanglement Entropy ◽  
Luttinger Liquid ◽  
High Energy ◽  
Duality Principle ◽  
Many Body ◽  
Tensor Network ◽  
Entropy Bound ◽  
The Many

Abstract We perform a unitary renormalization group (URG) study of the 1D fermionic Hubbard model. The formalism generates a family of effective Hamiltonians and many-body eigenstates arranged holographically across the tensor network from UV to IR. The URG is realized as a quantum circuit, leading to the entanglement holographic mapping (EHM) tensor network description. A topological Θ-term of the projected Hilbert space of the degrees of freedom at the Fermi surface are shown to govern the nature of RG flow towards either the gapless Tomonaga-Luttinger liquid or gapped quantum liquid phases. This results in a nonperturbative version of the Berezenskii-Kosterlitz-Thouless (BKT) RG phase diagram, revealing a line of intermediate coupling stable fixed points, while the nature of RG flow around the critical point is identical to that obtained from the weak-coupling RG analysis. This coincides with a phase transition in the many-particle entanglement, as the entanglement entropy RG flow shows distinct features for the critical and gapped phases depending on the value of the topological Θ-term. We demonstrate the Ryu-Takyanagi entropy bound for the many-body eigenstates comprising the EHM network, concretizing the relation to the holographic duality principle. The scaling of the entropy bound also distinguishes the gapped and gapless phases, implying the generation of very different holographic spacetimes across the critical point. Finally, we treat the Fermi surface as a quantum impurity coupled to the high energy electronic states. A thought-experiment is devised in order to study entanglement entropy generated by isolating the impurity, and propose ways by which to measure it by studying the quantum noise and higher order cumulants of the full counting statistics.

scholarly journals Entanglement and Disordered-Enhanced Topological Phase in the Kitaev Chain

Universe ◽  
2019 ◽  
Vol 5 (1) ◽  
pp. 33 ◽  
Author(s):  
Liron Levy ◽  
Moshe Goldstein
Keyword(s):  
Phase Diagram ◽  
Information Theory ◽  
Quantum Information ◽  
Critical Point ◽  
Entanglement Entropy ◽  
Quantum Information Theory ◽  
Topological Phase ◽  
Many Body ◽  
Zero Modes ◽  
Many Body Systems

In recent years, tools from quantum information theory have become indispensable in characterizing many-body systems. In this work, we employ measures of entanglement to study the interplay between disorder and the topological phase in 1D systems of the Kitaev type, which can host Majorana end modes at their edges. We find that the entanglement entropy may actually increase as a result of disorder, and identify the origin of this behavior in the appearance of an infinite-disorder critical point. We also employ the entanglement spectrum to accurately determine the phase diagram of the system, and find that disorder may enhance the topological phase, and lead to the appearance of Majorana zero modes in systems whose clean version is trivial.

scholarly journals Signatures of a critical point in the many-body localization transition

2021 ◽  
Vol 10 (5) ◽  
Author(s):  
Ángel L. Corps ◽  
Rafael Molina ◽  
Armando Relaño
Keyword(s):  
Singular Point ◽  
Critical Point ◽  
Chaotic Behavior ◽  
Finite Size ◽  
System Size ◽  
Disorder Strength ◽  
Many Body ◽  
Localization Transition ◽  
Spectral Statistics ◽  
The Many

Disordered interacting spin chains that undergo a many-body localization transition are characterized by two limiting behaviors where the dynamics are chaotic and integrable. However, the transition region between them is not fully understood yet. We propose here a possible finite-size precursor of a critical point that shows a typical finite-size scaling and distinguishes between two different dynamical phases. The kurtosis excess of the diagonal fluctuations of the full one-dimensional momentum distribution from its microcanonical average is maximum at this singular point in the paradigmatic disordered J_1J1-J_2J2 model. For system sizes accessible to exact diagonalization, both the position and the size of this maximum scale linearly with the system size. Furthermore, we show that this singular point is found at the same disorder strength at which the Thouless and the Heisenberg energies coincide. Below this point, the spectral statistics follow the universal random matrix behavior up to the Thouless energy. Above it, no traces of chaotic behavior remain, and the spectral statistics are well described by a generalized semi-Poissonian model, eventually leading to the integrable Poissonian behavior. We provide, thus, an integrated scenario for the many-body localization transition, conjecturing that the critical point in the thermodynamic limit, if it exists, should be given by this value of disorder strength.

Modeling of supersonic crowdion clusters in FCC lattice: Effect of the interatomic potential

2021 ◽  
pp. 2050019
Author(s):  
Igor A. Shelepev ◽  
Ayrat M. Bayazitov ◽  
Elena A. Korznikova
Keyword(s):  
Interatomic Potential ◽  
High Energy ◽  
Propagation Path ◽  
Interatomic Potentials ◽  
Energy Localization ◽  
Many Body ◽  
Embedded Atom ◽  
Fcc Lattice ◽  
The Many ◽  
Body Potential

Among a wide variety of point defects, crowdions can be distinguished by their high energy of formation and relatively low migration barriers, which makes them an important agent of mass transfer in lattices subjected to severe plastic deformation, irradiation, etc. It was previously shown that complexes and clusters of crowdions are even more mobile than single interstitials, which opened new mechanisms for the transfer of energy and mass in materials under intense external impacts. One of the most popular and convenient methods for analyzing crowdions is molecular dynamics, where the results can strongly depend on the interatomic potential used in the study. In this work, we compare the characteristics of a crowdion in an fcc lattice obtained using two different interatomic potentials — the pairwise Morse potential and the many-body potential for Al developed by the embedded atom method. It was found that the use of the many-body potential significantly affects the dynamics of crowdion propagation, including the features of atomic collisions, the evolution of energy localization and the propagation path.

Magnetic field dependence of the many-body enhancement on the Fermi surface of CeB6

1988 ◽  
Vol 76-77 ◽  
pp. 35-36 ◽  
Author(s):  
T. Müller ◽  
W. Joss ◽  
J.M. van Ruitenbeek ◽  
U. Welp ◽  
P. Wyder ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Fermi Surface ◽  
Field Dependence ◽  
Magnetic Field Dependence ◽  
Many Body ◽  
The Many ◽  
Body Enhancement

scholarly journals Quantum chaos on a critical Fermi surface

2017 ◽  
Vol 114 (8) ◽  
pp. 1844-1849 ◽  
Author(s):  
Aavishkar A. Patel ◽  
Subir Sachdev
Keyword(s):  
Fermi Surface ◽  
Quantum Chaos ◽  
Random Phase ◽  
Gauge Coupling ◽  
High Energy ◽  
Fermi Velocity ◽  
Coupling Constant ◽  
Many Body ◽  
Spatial Dimensions ◽  
The Relationship

We compute parameters characterizing many-body quantum chaos for a critical Fermi surface without quasiparticle excitations. We examine a theory ofNspecies of fermions at nonzero density coupled to aU(1)gauge field in two spatial dimensions and determine the Lyapunov rate and the butterfly velocity in an extended random-phase approximation. The thermal diffusivity is found to be universally related to these chaos parameters; i.e., the relationship is independent ofN, the gauge-coupling constant, the Fermi velocity, the Fermi surface curvature, and high-energy details.

STRANGE METALS AND HOLOGRAPHIC ENTANGLEMENT ENTROPY

2013 ◽  
Vol 28 (03n04) ◽  
pp. 1340004 ◽  
Author(s):  
TADASHI TAKAYANAGI
Keyword(s):  
Fermi Surface ◽  
High Energy Phys ◽  
Classical Limit ◽  
Entanglement Entropy ◽  
High Energy ◽  
Fermi Liquids ◽  
Surface Physics ◽  
Holographic Entanglement Entropy ◽  
Gravity Duals

In this paper, we will explain an application of holographic entanglement entropy to Fermi surface physics. These holographic arguments show that Landau–Fermi liquids do not have any gravity duals in the purely classical limit [N. Ogawa, T. Takayanagi and T. Ugajin, J. High Energy Phys.125, 1 (2012), arXiv:1111.1023 [hep-th]].

Anisotropy of the many-body enhancements on the Fermi surface of Pd

1984 ◽  
Vol 30 (10) ◽  
pp. 5646-5654 ◽  
Author(s):  
W. Joss ◽  
G. W. Crabtree
Keyword(s):  
Fermi Surface ◽  
Many Body ◽  
The Many

scholarly journals Many-Body Localization and the Emergence of Quantum Darwinism

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1377
Author(s):  
Nicolás Mirkin ◽  
Diego A. Wisniacki
Keyword(s):  
Quantum System ◽  
Entanglement Entropy ◽  
Redundant Information ◽  
Many Body ◽  
Initial State ◽  
Mobility Edge ◽  
Critical Degree ◽  
Quantum Darwinism ◽  
Effect Of Disorder ◽  
The Many

Quantum Darwinism (QD) is the process responsible for the proliferation of redundant information in the environment of a quantum system that is being decohered. This enables independent observers to access separate environmental fragments and reach consensus about the system’s state. In this work, we study the effect of disorder in the emergence of QD and find that a highly disordered environment is greatly beneficial for it. By introducing the notion of lack of redundancy to quantify objectivity, we show that it behaves analogously to the entanglement entropy (EE) of the environmental eigenstate taken as an initial state. This allows us to estimate the many-body mobility edge by means of our Darwinistic measure, implicating the existence of a critical degree of disorder beyond which the degree of objectivity rises the larger the environment is. The latter hints the key role that disorder may play when the environment is of a thermodynamic size. At last, we show that a highly disordered evolution may reduce the spoiling of redundancy in the presence of intra-environment interactions.

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