scholarly journals Unconventional phase separation in the model 2D spin-pseudospin system

2018 ◽  
Vol 185 ◽  
pp. 11006 ◽  
Author(s):  
K.S. Budrin ◽  
Yu.D. Panov ◽  
A.S. Moskvin ◽  
A.A. Chikov
Keyword(s):  
Monte Carlo ◽  
Phase Separation ◽  
Ground State ◽  
Spin Exchange ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Spin Subsystem ◽  
Monte Carlo Calculations ◽  
Antiferromagnetic Ordering

The competition of charge and spin orderings is a challenging problem for strongly correlated systems, in particular, for high-Tc cuprates. We addressed a simplified static 2D spin-pseudospin model which takes into account both conventional spin exchange coupling and the on-site and inter-site charge correlations. Classical Monte-Carlo calculations for large square lattices show that homogeneous ground state antiferromagnetic solutions found in a mean-field approximation are unstable with respect to phase separation into the charge and spin subsystems behaving like immiscible quantum liquids. In this case, with lowering of a temperature one can observe two sequential phase transitions: first, antiferromagnetic ordering in the spin subsystem diluted by randomly distributed charges, then, the charge condensation in the charge droplets. The inhomogeneous droplet phase reduces the energy of the system and changes the diagram of the ground states. On the other hand, the ground state energy of charge-ordered state in a mean-field approximation exactly matches the numerical Monte-Carlo calculations. The doped charges in this case are distributed randomly over a system in the whole temperature range. Various thermodynamic properties of the 2D spin-pseudospin system are studied by Monte-Carlo simulation.

KINETIC ENERGY AND PHASE SEPARATION IN A DOPED ANTIFERROMAGNET

1995 ◽  
Vol 09 (24) ◽  
pp. 1623-1629 ◽  
Author(s):  
XIN XU ◽  
YUN SONG ◽  
SHIPING FENG
Keyword(s):  
Phase Separation ◽  
Kinetic Energy ◽  
Ground State ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Numerical Result ◽  
The Mean ◽  
State Kinetic

The ground-state kinetic energy of the t-J model is studied within the mean field approximation by using the fermion-spin transformation, the results show that the mean field ground-state kinetic energy is close to the numerical result at under dopings, and roughly consistent with the numerical result at optimal dopings. It is also shown that the frustration term J′ is favourable to diminish the range of the phase seperation in the t-J model.

ASYMMETRIC EXCLUSION PROCESSES ON LATTICES WITH A JUNCTION: THE EFFECT OF UNEQUAL INJECTION RATES

2009 ◽  
Vol 20 (06) ◽  
pp. 967-978 ◽  
Author(s):  
XIONG WANG ◽  
RUI JIANG ◽  
KATSUHIRO NISHINARI ◽  
MAO-BIN HU ◽  
QING-SONG WU
Keyword(s):  
Phase Diagram ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Exclusion Processes ◽  
Asymmetric Exclusion ◽  
Asymmetric Exclusion Processes ◽  
Injection Rates

Asymmetric exclusion processes (ASEP) on lattices with a junction, in which two or more parallel lattice branches combine into a single one, is important as a model for complex transport phenomena. This paper investigates the effect of unequal injection rates in ASEP with a junction. It is a generalization of the work of Pronina and Kolomeisky [J. Stat. Mech. P07010 (2005)], in which only equal injection rates are considered. It is shown that the unequal rates give rise to new phases and the phase diagram structure is qualitatively changed. The phase diagram and the density profiles are investigated by using Monte Carlo simulations, mean field approximation and domain wall approach. The analytical results are in good agreement with Monte Carlo simulations.

Unraveling the origin of higher success probabilities in quantum annealing versus semi-classical annealing

2022 ◽  
Author(s):  
Elias Andre Starchl ◽  
Helmut Ritsch
Keyword(s):  
Hilbert Space ◽  
Ground State ◽  
Mean Field ◽  
Optimal Solution ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Quantum Model ◽  
Local Defect ◽  
Quantum Annealing ◽  
Full Quantum

Abstract Quantum annealing aims at finding optimal solutions to complex optimization problems using a suitable quantum many body Hamiltonian encoding the solution in its ground state. To find the solution one typically evolves the ground state of a soluble, simple initial Hamiltonian adiabatically to the ground state of the designated final Hamiltonian. Here we explore whether and when a full quantum representation of the dynamics leads to higher probability to end up in the desired ground when compared to a classical mean field approximation. As simple but nontrivial example we target the ground state of interacting bosons trapped in a tight binding lattice with small local defect by turning on long range interactions. Already two atoms in four sites interacting via two cavity modes prove complex enough to exhibit significant differences between the full quantum model and a mean field approximation for the cavity fields mediating the interactions. We find a large parameter region of highly successful quantum annealing, where the semi-classical approach largely fails. Here we see strong evidence for the importance of entanglement to end close to the optimal solution. The quantum model also reduces the minimal time for a high target occupation probability. Surprisingly, in contrast to naive expectations that enlarging the Hilbert space is beneficial, different numerical cut-offs of the Hilbert space reveal an improved performance for lower cut-offs, i.e. an nonphysical reduced Hilbert space, for short simulation times. Hence a less faithful representation of the full quantum dynamics sometimes creates a higher numerical success probability in even shorter time. However, a sufficiently high cut-off proves relevant to obtain near perfect fidelity for long simulations times in a single run. Overall our results exhibit a clear improvement to find the optimal solution based on a quantum model versus simulations based on a classical field approximation.

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