scholarly journals Overcoming the sign problem at finite temperature: Quantum tensor network for the orbital eg model on an infinite square lattice

2017 ◽  
Vol 96 (1) ◽  
Author(s):  
Piotr Czarnik ◽  
Jacek Dziarmaga ◽  
Andrzej M. Oleś
Keyword(s):  
Finite Temperature ◽  
Square Lattice ◽  
Sign Problem ◽  
Tensor Network

scholarly journals Finite temperature properties and frustrated ferromagnetism in a square lattice Heisenberg model

2004 ◽  
Vol 38 (4) ◽  
pp. 599-616 ◽  
Author(s):  
N. Shannon ◽  
B. Schmidt ◽  
K. Penc ◽  
P. Thalmeier
Keyword(s):  
Finite Temperature ◽  
Heisenberg Model ◽  
Square Lattice

scholarly journals QUANTUM MONTE CARLO METHODS FOR NUCLEI AT FINITE TEMPERATURE

2001 ◽  
Vol 15 (10n11) ◽  
pp. 1447-1462 ◽  
Author(s):  
Y. ALHASSID
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Methods ◽  
Finite Temperature ◽  
Quantum Monte Carlo ◽  
Configuration Spaces ◽  
Many Body ◽  
Level Densities ◽  
Sign Problem ◽  
Quantum Monte Carlo Methods ◽  
Nuclear Shell

We discuss finite temperature quantum Monte Carlo methods in the framework of the interacting nuclear shell model. The methods are based on a representation of the imaginary-time many-body propagator as a superposition of one-body propagators describing non-interacting fermions moving in fluctuating auxiliary fields. Fermionic Monte Carlo calculations have been limited by a "sign" problem. A practical solution in the nuclear case enables realistic calculations in much larger configuration spaces than can be solved by conventional methods. Good-sign interactions can be constructed for realistic estimates of certain nuclear properties. We present various applications of the methods for calculating collective properties and level densities.

scholarly journals Spin wave theory of spin-1/2 XY model with ring exchange on a triangular lattice

2013 ◽  
Vol 91 (7) ◽  
pp. 542-547 ◽  
Author(s):  
Solomon A. Owerre
Keyword(s):  
Phase Transition ◽  
Spin Wave ◽  
Triangular Lattice ◽  
Finite Temperature ◽  
Wave Theory ◽  
Square Lattice ◽  
Xy Model ◽  
Superfluid Phase ◽  
Zero Temperature ◽  
Ring Exchange

We present the linear spin wave theory calculation of the superfluid phase of a hard-core boson J-K model with nearest neighbour exchange J and four-particle ring-exchange K at half filling on the triangular lattice, as well as the phase diagrams of the system at zero and finite temperatures. A similar analysis has been done on a square lattice (Schaffer et al. Phys. Rev. B, 80, 014503 (2009)). We find similar behaviour to that of a square lattice but with different spin wave values of the thermodynamic quantities. We also find that the pure J model (XY model), which has a well-known uniform superfluid phase with an ordered parameter [Formula: see text] at zero temperature is quickly destroyed by the inclusion of negative-K ring-exchange interactions, favouring a state with a (4π/3, 0) ordering wavevector. We further study the behaviour of the finite-temperature Kosterlitz–Thouless phase transition (TKT) in the uniform superfluid phase, by forcing the universal quantum jump condition on the finite-temperature spin wave superfluid density. We find that for K < 0, the phase boundary monotonically decreases to T = 0 at K/J = −4/3, where a phase transition is expected and TKT decreases rapidly, while for positive K, TKT reaches a maximum at some K ≠ 0. It has been shown on a square lattice using quantum Monte Carlo (QMC) simulations that for small K > 0 away from the XY point, the zero-temperature spin stiffness value of the XY model is decreased (Melko and Sandvik. Ann. Phys. 321, 1651 (2006)). Our result seems to agree with this trend found in QMC simulations for two-dimensional systems.

scholarly journals Lattice QCD at Finite Temperature and Density

2007 ◽  
Vol 22 (07n10) ◽  
pp. 457-471 ◽  
Author(s):  
M. P. LOMBARDO
Keyword(s):  
Lattice Qcd ◽  
Finite Temperature ◽  
Taylor Expansion ◽  
Critical Line ◽  
Chemical Potential ◽  
Normal Phase ◽  
Theoretical Physics ◽  
General Introduction ◽  
Sign Problem ◽  
The Subject

A general introduction into the subject aimed at a general theoretical physics audience. We introduce the sign problem posed by finite density lattice QCD, and we discuss the main methods proposed to circumvent it, with emphasis on the imaginary chemical potential approach. The interrelation between Taylor expansion and analytic continuation from imaginary chemical potential is discussed in detail. The main applications to the calculation of the critical line, and to the thermodynamics of the hot and normal phase are reviewed.

scholarly journals A beginner's guide to non-abelian iPEPS for correlated fermions

2021 ◽  
Author(s):  
Benedikt Bruognolo ◽  
Jheng-Wei Li ◽  
Jan von Delft ◽  
Andreas Weichselbaum
Keyword(s):  
Lattice Models ◽  
Square Lattice ◽  
Special Focus ◽  
Two Dimensional ◽  
Technical Advance ◽  
Hubbard Models ◽  
Tensor Network ◽  
Fermionic Systems ◽  
Correlated Fermions ◽  
Multi Band

Infinite projected entangled pair states (iPEPS) have emerged as a powerful tool for studying interacting two-dimensional fermionic systems. In this review, we discuss the iPEPS construction and some basic properties of this tensor network (TN) ansatz. Special focus is put on (i) a gentle introduction of the diagrammatic TN representations forming the basis for deriving the complex numerical algorithm, and (ii) the technical advance of fully exploiting non-abelian symmetries for fermionic iPEPS treatments of multi-band lattice models. The exploitation of non-abelian symmetries substantially increases the performance of the algorithm, enabling the treatment of fermionic systems up to a bond dimension D=24D=24 on a square lattice. A variety of complex two-dimensional (2D) models thus become numerically accessible. Here, we present first promising results for two types of multi-band Hubbard models, one with 22 bands of spinful fermions of \mathrm{SU}(2)_\mathrm{spin} \otimes \mathrm{SU}(2)_\mathrm{orb}SU(2)spin⊗SU(2)orb symmetry, the other with 33 flavors of spinless fermions of \mathrm{SU}(3)_\mathrm{flavor}SU(3)flavor symmetry.

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