scholarly journals Finite-temperature symmetric tensor network for spin-1/2 Heisenberg antiferromagnets on the square lattice

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Didier Poilblanc ◽  
Matthieu Mambrini ◽  
Fabien Alet
Keyword(s):  
Finite Temperature ◽  
Symmetric Tensor ◽  
Square Lattice ◽  
Tensor Network ◽  
Heisenberg Antiferromagnets

scholarly journals The classical two-dimensional Heisenberg model revisited: An $SU(2)$-symmetric tensor network study

2021 ◽  
Vol 11 (5) ◽  
Author(s):  
Philipp Schmoll ◽  
Augustine Kshetrimayum ◽  
Jens Eisert ◽  
Román Orús ◽  
Matteo Rizzi
Keyword(s):  
Finite Temperature ◽  
Heisenberg Model ◽  
Symmetric Tensor ◽  
Linear Sigma Model ◽  
Asymptotic Freedom ◽  
Quantum Field Theories ◽  
Two Dimensional ◽  
Tensor Network ◽  
Spatial Dimensions ◽  
Contraction Scheme

The classical Heisenberg model in two spatial dimensions constitutes one of the most paradigmatic spin models, taking an important role in statistical and condensed matter physics to understand magnetism. Still, despite its paradigmatic character and the widely accepted ban of a (continuous) spontaneous symmetry breaking, controversies remain whether the model exhibits a phase transition at finite temperature. Importantly, the model can be interpreted as a lattice discretization of the O(3)O(3) non-linear sigma model in 1+11+1 dimensions, one of the simplest quantum field theories encompassing crucial features of celebrated higher-dimensional ones (like quantum chromodynamics in 3+13+1 dimensions), namely the phenomenon of asymptotic freedom. This should also exclude finite-temperature transitions, but lattice effects might play a significant role in correcting the mainstream picture. In this work, we make use of state-of-the-art tensor network approaches, representing the classical partition function in the thermodynamic limit over a large range of temperatures, to comprehensively explore the correlation structure for Gibbs states. By implementing an SU(2)SU(2) symmetry in our two-dimensional tensor network contraction scheme, we are able to handle very large effective bond dimensions of the environment up to \chi_E^\text{eff} \sim 1500χEeff∼1500, a feature that is crucial in detecting phase transitions. With decreasing temperatures, we find a rapidly diverging correlation length, whose behaviour is apparently compatible with the two main contradictory hypotheses known in the literature, namely a finite-TT transition and asymptotic freedom, though with a slight preference for the second.

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 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 Spin Dependence of Correlations in Two-Dimensional Square-Lattice Quantum Heisenberg Antiferromagnets

1995 ◽  
Vol 75 (5) ◽  
pp. 938-941 ◽  
Author(s):  
N. Elstner ◽  
A. Sokol ◽  
R. R. P. Singh ◽  
M. Greven ◽  
R. J. Birgeneau
Keyword(s):  
Square Lattice ◽  
Two Dimensional ◽  
Spin Dependence ◽  
Lattice Quantum ◽  
Heisenberg Antiferromagnets

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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