scholarly journals Thermal tensor network simulations of the Heisenberg model on the Bethe lattice

2019 ◽  
Vol 100 (12) ◽  
Author(s):  
Dai-Wei Qu ◽  
Wei Li ◽  
Tao Xiang
Keyword(s):  
Heisenberg Model ◽  
Bethe Lattice ◽  
Tensor Network ◽  
Network Simulations

scholarly journals Tangent-space methods for truncating uniform MPS

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Bram Vanhecke ◽  
Maarten Van Damme ◽  
Jutho Haegeman ◽  
Laurens Vanderstraeten ◽  
Frank Verstraete
Keyword(s):  
Tangent Space ◽  
Computational Cost ◽  
Infinite Matrix ◽  
Matrix Product ◽  
Product State ◽  
Matrix Product State ◽  
Product Operator ◽  
Tensor Network ◽  
Network Simulations ◽  
Central Bottleneck

An essential primitive in quantum tensor network simulations is the problem of approximating a matrix product state with one of a smaller bond dimension. This problem forms the central bottleneck in algorithms for time evolution and for contracting projected entangled pair states. We formulate a tangent-space based variational algorithm to achieve this goal for uniform (infinite) matrix product states. The algorithm exhibits a favourable scaling of the computational cost, and we demonstrate its usefulness by several examples involving the multiplication of a matrix product state with a matrix product operator.

scholarly journals Probabilistic low-rank factorization accelerates tensor network simulations of critical quantum many-body ground states

2018 ◽  
Vol 97 (1) ◽  
Author(s):  
Lucas Kohn ◽  
Ferdinand Tschirsich ◽  
Maximilian Keck ◽  
Martin B. Plenio ◽  
Dario Tamascelli ◽  
...  
Keyword(s):  
Ground States ◽  
Low Rank ◽  
Many Body ◽  
Tensor Network ◽  
Network Simulations ◽  
Rank Factorization

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 Spin-$\frac{1}{2}$ kagome Heisenberg antiferromagnet with strong breathing anisotropy

2020 ◽  
Vol 9 (6) ◽  
Author(s):  
Saeed Jahromi ◽  
Roman Orus ◽  
Didier Poilblanc ◽  
Frédéric Mila
Keyword(s):  
Heisenberg Model ◽  
Large Scale ◽  
Rotational Symmetry ◽  
Real Space ◽  
Quantum Spin ◽  
Temperature Phase ◽  
Kagome Lattice ◽  
Kagomé Lattice ◽  
Algebraic Quantum ◽  
Network Simulations

We study the zero-temperature phase diagram of the spin-1/2 Heisenberg model with breathing anisotropy (i.e., with different coupling strength on the upward and downward triangles) on the kagome lattice. Our study relies on large scale tensor network simulations based on infinite projected entangled-pair state and infinite projected entangled-simplex state methods adapted to the kagome lattice. Our energy analysis suggests that the U(1) algebraic quantum spin-liquid (QSL) ground-state of the isotropic Heisenberg model is stable up to very large breathing anisotropy until it breaks down to a critical lattice-nematic phase that breaks rotational symmetry in real space through a first-order quantum phase transition. Our results also provide further insight into the recent experiment on vanadium oxyfluoride compounds which has been shown to be relevant platforms for realizing QSL in the presence of breathing anisotropy.

scholarly journals A tensor network study of the complete ground state phase diagram of the spin-1 bilinear-biquadratic Heisenberg model on the square lattice

2017 ◽  
Vol 3 (4) ◽  
Author(s):  
Ido Niesen ◽  
Philippe Corboz
Keyword(s):  
Phase Diagram ◽  
Phase Transitions ◽  
Thermodynamic Limit ◽  
Ground State ◽  
Heisenberg Model ◽  
Magnetic Phase ◽  
Square Lattice ◽  
Ground State Phase Diagram ◽  
Tensor Network

Using infinite projected entangled pair states, we study the ground state phase diagram of the spin-1 bilinear-biquadratic Heisenberg model on the square lattice directly in the thermodynamic limit. We find an unexpected partially nematic partially magnetic phase in between the antiferroquadrupolar and ferromagnetic regions. Furthermore, we describe all observed phases and discuss the nature of the phase transitions involved.

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