36 research outputs found
Quantum Hertz entropy increase in a quenched spin chain
The classical Hertz entropy is the logarithm of the volume of phase space
bounded by the constant energy surface; its quantum counterpart, the quantum
Hertz entropy, is , where the quantum operator specifies the number of states with energy below a given energy eigenstate.
It has been recently proved that, when an isolated quantum mechanical system is
driven out of equilibrium by an external driving, the change in the expectation
of its quantum Hertz entropy cannot be negative, and is null for adiabatic
driving. This is in full agreement with the Clausius principle. Here we test
the behavior of the expectation of the quantum Hertz entropy in the case when
two identical XY spin chains initially at different temperatures are quenched
into a single XY chain. We observed no quantum Hertz entropy decrease. This
finding further supports the statement that the quantum Hertz entropy is a
proper entropy for isolated quantum systems. We further quantify how far the
quenched chain is from thermal equilibrium and the temperature of the closest
equilibrium.Comment: 9 pages, 5 figure
Superconductivity of non-Fermi liquids described by Sachdev-Ye-Kitaev models
We investigate models of electrons in the Sachdev-Ye-Kitaev class with random
and all-to-all electron hopping, electron spin exchange, and Cooper-pair
hopping. An attractive on-site interaction between electrons leads to
superconductivity at low temperatures. Depending on the relative strengths of
the hopping and spin exchange, the normal state at the critical temperature is
either a Fermi-liquid or a non-Fermi liquid. We present a large- (where spin
symmetry is enlarged to SU) study of the normal state to superconductor
phase transition. We describe the transition temperature, the superconducting
order parameter, and the electron spectral functions. We contrast between Fermi
liquid and non-Fermi liquid normal states: we find that for weaker attractive
on-site interaction there is a relative enhancement of when the normal
state is a non-Fermi liquid, and correspondingly a strong deviation from BCS
limit. Also, the phase transition in this case becomes a first-order transition
for strong non-Fermi liquids. On the other hand, for stronger on-site
interaction, there is no appreciable difference in between whether the
superconductivity emerges from a Fermi liquid or a non-Fermi liquid. Notable
features of superconductivity emerging from a non-Fermi liquid are that the
superconducting electron spectral function is different from the Fermi-liquid
case, with additional peaks at higher energies, and there is no Hebel-Slichter
peak in the NMR relaxation rate in the non-Fermi liquid case.Comment: 26 pages, 13 figures; (v2) Added new results, figures, and
references, modified abstract, and expanded discussio
Quantum disordered insulating phase in the frustrated cubic-lattice Hubbard model
In the quest for quantum spin liquids in three spatial dimensions (3D), we
study the half-filled Hubbard model on the simple cubic lattice with hopping
processes up to third neighbors. Employing the variational cluster approach
(VCA), we determine the zero-temperature phase diagram: In addition to a
paramagnetic metal at small interaction strength and various
antiferromagnetic insulators at large , we find an intermediate-
antiferromagnetic metal. Most interestingly, we also identify a non-magnetic
insulating region, extending from intermediate to strong . Using VCA results
in the large- limit, we establish the phase diagram of the corresponding
-- Heisenberg model. This is qualitatively confirmed - including
the non-magnetic region - using spin-wave theory. Further analysis reveals a
striking similarity to the behavior of the - square-lattice
Heisenberg model, suggesting that the non-magnetic region hosts a 3D
spin-liquid phase.Comment: 5 pages, 4 figures; final version incl. discussion about material