scholarly journals Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results

2020 ◽  
pp. 2060004
Author(s):  
Joscha Henheik ◽  
Stefan Teufel
Keyword(s):  
Transport Coefficients ◽  
Quantum Hall ◽  
Linear Response Theory ◽  
Quantum Systems ◽  
Stationary States ◽  
Zero Temperature ◽  
Theoretical Understanding ◽  
Adiabatic Theorem ◽  
Finite Lattices ◽  
Fermionic Systems

We first review the problem of a rigorous justification of Kubo’s formula for transport coefficients in gapped extended Hamiltonian quantum systems at zero temperature. In particular, the theoretical understanding of the quantum Hall effect rests on the validity of Kubo’s formula for such systems, a connection that we review briefly as well. We then highlight an approach to linear response theory based on non-equilibrium almost-stationary states (NEASS) and on a corresponding adiabatic theorem for such systems that was recently proposed and worked out by one of us in [51] for interacting fermionic systems on finite lattices. In the second part of our paper, we show how to lift the results of [51] to infinite systems by taking a thermodynamic limit.

scholarly journals Wiedemann-Franz laws and Sl(2, ℤ) duality in AdS/CMT holographic duals and one-dimensional effective actions for them

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Dmitry Melnikov ◽  
Horatiu Nastase
Keyword(s):  
Quantum Hall Effect ◽  
Effective Action ◽  
Transport Coefficients ◽  
Quantum Hall ◽  
Dual Theory ◽  
One Dimensional ◽  
Integer Quantum Hall Effect ◽  
Weakly Coupled ◽  
Holographic Duals ◽  
Integer Quantum

Abstract In this paper we study the Wiedemann-Franz laws for transport in 2+1 dimensions, and the action of Sl(2, ℤ) on this transport, for theories with an AdS/CMT dual. We find that Sl(2, ℤ) restricts the RG-like flow of conductivities and that the Wiedemann-Franz law is $$ \overline{L}=\overline{\kappa}/\left( T\sigma \right)={cg}_4^2\uppi /3 $$ L ¯ = κ ¯ / Tσ = cg 4 2 π / 3 , from the weakly coupled gravity dual. In a self-dual theory this value is also the value of L = κ/(Tσ) in the weakly coupled field theory description. Using the formalism of a 0+1 dimensional effective action for both generalized SY Kq models and the AdS4 gravity dual, we calculate the transport coefficients and show how they can be matched at large q. We construct a generalization of this effective action that is invariant under Sl(2, ℤ) and can describe vortex conduction and integer quantum Hall effect.

scholarly journals Residual Entropy and Critical Behavior of Two Interacting Boson Species in a Double Well

2017 ◽  
Author(s):  
Fabio Lingua ◽  
Andrea Richaud ◽  
Vittorio Penna
Keyword(s):  
Coherent States ◽  
Variational Approach ◽  
Entanglement Entropy ◽  
Quantum Systems ◽  
Residual Entropy ◽  
Zero Temperature ◽  
Temperature Scenario ◽  
Physical Insight ◽  
Insight Into ◽  
Specific Quantum

Motivated by the importance of entanglement and correlation indicators in the analysis of quantum systems, we study the equilibrium and the residual entropy in a two-species Bose Hubbard dimer when the spatial phase separation of the two species takes place. We consider both the zero and non-zero-temperature regime. We present different kinds of residual entropies (each one associated to a different way of partitioning the system), and we show that they strictly depend on the specific quantum phase characterizing the two species (supermixed, mixed or demixed) even at finite temperature. To provide a deeper physical insight into the zero-temperature scenario, we apply the fully-analytical variational approach based on su(2) coherent states and provide a considerbly good approximation of the entanglement entropy. Finally, we show that the effectiveness of residual entropy as a critical indicator at non-zero temperature is unchanged when considering a restricted combination of energy eigenstates.

Statistical Mechanics: Entropy, Order Parameters, and Complexity

2021 ◽  
Author(s):  
James P. Sethna
Keyword(s):  
Statistical Mechanics ◽  
Topological Defects ◽  
Linear Response Theory ◽  
Continuous Phase ◽  
Quantum Systems ◽  
Order Parameters ◽  
Free Energies ◽  
Onset Of Chaos ◽  
The Social ◽  
Essential Insight

This text distills the core ideas of statistical mechanics to make room for new advances important to information theory, complexity, active matter, and dynamical systems. Chapters address random walks, equilibrium systems, entropy, free energies, quantum systems, calculation and computation, order parameters and topological defects, correlations and linear response theory, and abrupt and continuous phase transitions. Exercises explore the enormous range of phenomena where statistical mechanics provides essential insight — from card shuffling to how cells avoid errors when copying DNA, from the arrow of time to animal flocking behavior, from the onset of chaos to fingerprints. The text is aimed at graduates, undergraduates, and researchers in mathematics, computer science, engineering, biology, and the social sciences as well as to physicists, chemists, and astrophysicists. As such, it focuses on those issues common to all of these fields, background in quantum mechanics, thermodynamics, and advanced physics should not be needed, although scientific sophistication and interest will be important.

Improved finite-lattice method for estimating the zero-temperature properties of two-dimensional lattice models

1996 ◽  
Vol 74 (1-2) ◽  
pp. 54-64 ◽  
Author(s):  
D. D. Betts ◽  
S. Masui ◽  
N. Vats ◽  
G. E. Stewart
Keyword(s):  
Spontaneous Magnetization ◽  
Finite Lattice ◽  
Quantum Spin ◽  
Square Lattice ◽  
Two Dimensional ◽  
Zero Temperature ◽  
Quantum Spin Systems ◽  
Lattice Method ◽  
Dimensional Lattice ◽  
Finite Lattices

The well-known finite-lattice method for the calculation of the properties of quantum spin systems on a two-dimensional lattice at zero temperature was introduced in 1978. The method has now been greatly improved for the square lattice by including finite lattices based on parallelogram tiles as well as the familiar finite lattices based on square tiles. Dozens of these new finite lattices have been tested and graded using the [Formula: see text] ferromagnet. In the process new and improved estimates have been obtained for the XY model's ground-state energy per spin, ε0 = −0.549 36(30) and spontaneous magnetization per spin, m = 0.4349(10). Other properties such as near-neighbour, zero-temperature spin–spin correlations, which appear not to have been calculated previously, have been estimated to high precision. Applications of the improved finite-lattice method to other models can readily be carried out.

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