scholarly journals Systematic construction of spin liquids on the square lattice from tensor networks with SU(2) symmetry

2016 ◽  
Vol 94 (20) ◽  
Author(s):  
Matthieu Mambrini ◽  
Román Orús ◽  
Didier Poilblanc
Keyword(s):  
Square Lattice ◽  
Spin Liquids ◽  
Systematic Construction ◽  
Tensor Networks

scholarly journals Thermal Hall effect in square-lattice spin liquids: A Schwinger boson mean-field study

2019 ◽  
Vol 99 (16) ◽  
Author(s):  
Rhine Samajdar ◽  
Shubhayu Chatterjee ◽  
Subir Sachdev ◽  
Mathias S. Scheurer
Keyword(s):  
Hall Effect ◽  
Field Study ◽  
Mean Field ◽  
Square Lattice ◽  
Spin Liquids ◽  
Lattice Spin

scholarly journals Efficient variational contraction of two-dimensional tensor networks with a non-trivial unit cell

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 328
Author(s):  
A. Nietner ◽  
B. Vanhecke ◽  
F. Verstraete ◽  
J. Eisert ◽  
L. Vanderstraeten
Keyword(s):  
Variational Principles ◽  
Valence Bond ◽  
Computational Effort ◽  
Unit Cell ◽  
Square Lattice ◽  
Partition Functions ◽  
Matrix Product ◽  
Two Dimensional ◽  
Matrix Product State ◽  
Tensor Networks

Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the description of such complex many-body systems, close to optimal variational principles based on such states are less obvious to come by. In this work, we generalize a recently proposed variational uniform matrix product state algorithm for capturing one-dimensional quantum lattices in the thermodynamic limit, to the study of regular two-dimensional tensor networks with a non-trivial unit cell. A key property of the algorithm is a computational effort that scales linearly rather than exponentially in the size of the unit cell. We demonstrate the performance of our approach on the computation of the classical partition functions of the antiferromagnetic Ising model and interacting dimers on the square lattice, as well as of a quantum doped resonating valence bond state.

scholarly journals Cavity-induced quantum spin liquids

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Alessio Chiocchetta ◽  
Dominik Kiese ◽  
Carl Philipp Zelle ◽  
Francesco Piazza ◽  
Sebastian Diehl
Keyword(s):  
Optical Cavity ◽  
Strongly Correlated Electrons ◽  
Quantum Spin ◽  
Square Lattice ◽  
Spin Liquids ◽  
Range Interaction ◽  
Quantum Spin Liquids ◽  
Electro Magnetic Field ◽  
Electro Magnetic ◽  
Liquid States

AbstractQuantum spin liquids provide paradigmatic examples of highly entangled quantum states of matter. Frustration is the key mechanism to favor spin liquids over more conventional magnetically ordered states. Here we propose to engineer frustration by exploiting the coupling of quantum magnets to the quantized light of an optical cavity. The interplay between the quantum fluctuations of the electro-magnetic field and the strongly correlated electrons results in a tunable long-range interaction between localized spins. This cavity-induced frustration robustly stabilizes spin liquid states, which occupy an extensive region in the phase diagram spanned by the range and strength of the tailored interaction. This occurs even in originally unfrustrated systems, as we showcase for the Heisenberg model on the square lattice.

scholarly journals Abelian SU(N)1 chiral spin liquids on the square lattice

2021 ◽  
Vol 104 (23) ◽  
Author(s):  
Ji-Yao Chen ◽  
Jheng-Wei Li ◽  
Pierre Nataf ◽  
Sylvain Capponi ◽  
Matthieu Mambrini ◽  
...  
Keyword(s):  
Square Lattice ◽  
Spin Liquids

scholarly journals Investigation of the Néel phase of the frustrated Heisenberg antiferromagnet by differentiable symmetric tensor networks

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Juraj Hasik ◽  
Didier Poilblanc ◽  
Federico Becca
Keyword(s):  
Automatic Differentiation ◽  
Symmetric Tensor ◽  
Extensive Study ◽  
Square Lattice ◽  
Antiferromagnetic Order ◽  
Heisenberg Antiferromagnet ◽  
Frustrated Magnetism ◽  
Magnetic Systems ◽  
Tensor Networks ◽  
Consistent Picture

The recent progress in the optimization of two-dimensional tensor networks [H.-J. Liao, J.-G. Liu, L. Wang, and T. Xiang, Phys. Rev. X 9, 031041 (2019)] based on automatic differentiation opened the way towards precise and fast optimization of such states and, in particular, infinite projected entangled-pair states (iPEPS) that constitute a generic-purpose Ansatz for lattice problems governed by local Hamiltonians. In this work, we perform an extensive study of a paradigmatic model of frustrated magnetism, the J_1-J_2J1−J2 Heisenberg antiferromagnet on the square lattice. By using advances in both optimization and subsequent data analysis, through finite correlation-length scaling, we report accurate estimations of the magnetization curve in the N'eel phase for J_2/J_1 \le 0.45J2/J1≤0.45. The unrestricted iPEPS simulations reveal an U(1)U(1) symmetric structure, which we identify and impose on tensors, resulting in a clean and consistent picture of antiferromagnetic order vanishing at the phase transition with a quantum paramagnet at J_2/J_1 \approx 0.46(1)J2/J1≈0.46(1). The present methodology can be extended beyond this model to study generic order-to-disorder transitions in magnetic systems.

Influence of Flexible Side-Chains on the Breathing Phase Transition of Pillared Layer MOFs: A Force Field Investigation

2020 ◽  
Author(s):  
Julian Keupp ◽  
Johannes P. Dürholt ◽  
Rochus Schmid
Keyword(s):  
First Principles ◽  
Good Accuracy ◽  
Field Investigation ◽  
Square Lattice ◽  
Side Chain ◽  
Second Step ◽  
Side Chains ◽  
Dynamics Simulations ◽  
Complex Phenomena ◽  
Closed Pore

The prototypical pillared layer MOFs, formed by a square lattice of paddle-<br>wheel units and connected by dinitrogen pillars, can undergo a breathing phase<br>transition by a “wine-rack” type motion of the square lattice. We studied this not<br>yet fully understood behavior using an accurate first principles parameterized force<br>field (MOF-FF) for larger nanocrystallites on the example of Zn 2 (bdc) 2 (dabco) [bdc:<br>benzenedicarboxylate, dabco: (1,4-diazabicyclo[2.2.2]octane)] and found clear indi-<br>cations for an interface between a closed and an open pore phase traveling through<br>the system during the phase transformation [Adv. Theory Simul. 2019, 2, 11]. In<br>conventional simulations in small supercells this mechanism is prevented by periodic<br>boundary conditions (PBC), enforcing a synchronous transformation of the entire<br>crystal. Here, we extend this investigation to pillared layer MOFs with flexible<br>side-chains, attached to the linker. Such functionalized (fu-)MOFs are experimen-<br>tally known to have different properties with the side-chains acting as fixed guest<br>molecules. First, in order to extend the parameterization for such flexible groups,<br>1a new parametrization strategy for MOF-FF had to be developed, using a multi-<br>structure force based fit method. The resulting parametrization for a library of<br>fu-MOFs is then validated with respect to a set of reference systems and shows very<br>good accuracy. In the second step, a series of fu-MOFs with increasing side-chain<br>length is studied with respect to the influence of the side-chains on the breathing<br>behavior. For small supercells in PBC a systematic trend of the closed pore volume<br>with the chain length is observed. However, for a nanocrystallite model a distinct<br>interface between a closed and an open pore phase is visible only for the short chain<br>length, whereas for longer chains the interface broadens and a nearly concerted trans-<br>formation is observed. Only by molecular dynamics simulations using accurate force<br>fields such complex phenomena can be studied on a molecular level.

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