scholarly journals Emergence of generalized hydrodynamics in the non-local Luttinger model

2020 ◽  
Vol 9 (3) ◽  
Author(s):  
Per Moosavi
Keyword(s):  
Formal Proof ◽  
Many Body ◽  
Recent Proposal ◽  
Perfect Agreement ◽  
Luttinger Model ◽  
Generalized Hydrodynamics ◽  
Long Range Interactions ◽  
Exactly Solvable ◽  
Solvable Quantum ◽  
Non Local

We propose the Luttinger model with finite-range interactions as a simple tractable example in 1+1 dimensions to analytically study the emergence of Euler-scale hydrodynamics in a quantum many-body system. This non-local Luttinger model is an exactly solvable quantum field theory somewhere between conformal and Bethe-ansatz integrable models. Applying the recent proposal of generalized hydrodynamics, we show that the model allows for fully explicit yet non-trivial solutions of the resulting Euler-scale hydrodynamic equations. Comparing with exact analytical non-equilibrium results valid at all time and length scales, we show perfect agreement at the Euler scale when the interactions are short range. A formal proof of the emergence of generalized hydrodynamics in the non-local Luttinger model is also given, and effects of long-range interactions are briefly discussed.

scholarly journals Entanglement and the Born-Oppenheimer approximation in an exactly solvable quantum many-body system

2014 ◽  
Vol 68 (11) ◽  
Author(s):  
Peter A. Bouvrie ◽  
Ana P. Majtey ◽  
Malte C. Tichy ◽  
Jesus S. Dehesa ◽  
Angel R. Plastino
Keyword(s):  
Body System ◽  
Many Body ◽  
Exactly Solvable ◽  
Solvable Quantum ◽  
Oppenheimer Approximation

scholarly journals Interaction between Different Kinds of Quantum Phase Transitions

2021 ◽  
Vol 3 (2) ◽  
pp. 253-261
Author(s):  
Angel Ricardo Plastino ◽  
Gustavo Luis Ferri ◽  
Angelo Plastino
Keyword(s):  
Phase Transitions ◽  
Nuclear Physics ◽  
Body Problem ◽  
Quantum Phase Transitions ◽  
Quantum Phase ◽  
Exactly Solvable Models ◽  
Solvable Models ◽  
Many Body ◽  
Pairing Interaction ◽  
Exactly Solvable

We employ two different Lipkin-like, exactly solvable models so as to display features of the competition between different fermion–fermion quantum interactions (at finite temperatures). One of our two interactions mimics the pairing interaction responsible for superconductivity. The other interaction is a monopole one that resembles the so-called quadrupole one, much used in nuclear physics as a residual interaction. The pairing versus monopole effects here observed afford for some interesting insights into the intricacies of the quantum many body problem, in particular with regards to so-called quantum phase transitions (strictly, level crossings).

Many-body forces in exactly solvable field-theoretical models

1975 ◽  
Vol 25 (3) ◽  
pp. 288-301 ◽  
Author(s):  
F. Calogero ◽  
D. De Santis
Keyword(s):  
Theoretical Models ◽  
Many Body ◽  
Body Forces ◽  
Exactly Solvable

scholarly journals Analysis of the buildup of spatiotemporal correlations and their bounds outside of the light cone

2018 ◽  
Vol 5 (5) ◽  
Author(s):  
Nils O. Abeling ◽  
Lorenzo Cevolani ◽  
Stefan Kehrein
Keyword(s):  
Correlation Function ◽  
Power Law ◽  
Light Cone ◽  
Relativistic Quantum ◽  
Initial State ◽  
Quantum Theories ◽  
Luttinger Model ◽  
Power Law Decay ◽  
Exactly Solvable ◽  
Exponentially Small

In non-relativistic quantum theories the Lieb-Robinson bound defines an effective light cone with exponentially small tails outside of it. In this work we use it to derive a bound for the correlation function of two local disjoint observables at different times if the initial state has a power-law decay. We show that the exponent of the power-law of the bound is identical to the initial (equilibrium) decay. We explicitly verify this result by studying the full dynamics of the susceptibilities and correlations in the exactly solvable Luttinger model after a sudden quench from the non-interacting to the interacting model.

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