Probing the stability of the spin liquid phases in the Kitaev-Heisenberg model using tensor network algorithms

We study the extent of the spin liquid phases in the Kitaev-Heisenberg model using infinite Projected Entangled-Pair States tensor network ansatz wave functions directly in the thermodynamic limit. To assess the accuracy of the ansatz wave functions we perform benchmarks against exact results for the Kitaev model and find very good agreement for various observables. In the case of the Kitaev-Heisenberg model we confirm the existence of 6 different phases: N\'eel, stripy, ferromagnetic, zigzag and two spin liquid phases. We find finite extents for both spin liquid phases and discontinuous phase transitions connecting them to symmetry-broken phases.Comment: 9 pages, 7 figures. Adjusted notation in equations 4-8. Added bond labeling to lower panel in figure 1. Included missing acknowledgement

Infinite Matrix Product States vs Infinite Projected Entangled-Pair States on the Cylinder: a comparative study

In spite of their intrinsic one-dimensional nature matrix product states have been systematically used to obtain remarkably accurate results for two-dimensional systems. Motivated by basic entropic arguments favoring projected entangled-pair states as the method of choice, we assess the relative performance of infinite matrix product states and infinite projected entangled-pair states on cylindrical geometries. By considering the Heisenberg and half-filled Hubbard models on the square lattice as our benchmark cases, we evaluate their variational energies as a function of both bond dimension as well as cylinder width. In both examples we find crossovers at moderate cylinder widths, i.e. for the largest bond dimensions considered we find an improvement on the variational energies for the Heisenberg model by using projected entangled-pair states at a width of about 11 sites, whereas for the half-filled Hubbard model this crossover occurs at about 7 sites.Comment: 11 pages, 9 figure

UvA-DARE (Digital Academic Repository) Probing the stability of the spin-liquid phases in the Kitaev-Heisenberg model using tensor network algorithms

Probing the stability of the spin liquid phases in the Kitaev-Heisenberg model using tensor network algorithms Iregui, J.O.; Corboz, P.R.; Troyer, M. General rights It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. We study the extent of the spin liquid phases in the Kitaev-Heisenberg model using infinite projected entangledpair states tensor network ansatz wave functions directly in the thermodynamic limit. To assess the accuracy of the ansatz wave functions, we perform benchmarks against exact results for the Kitaev model and find very good agreement for various observables. In the case of the Kitaev-Heisenberg model, we confirm the existence of six different phases: Néel, stripy, ferromagnetic, zigzag, and two spin liquid phases. We find finite extents for both spin liquid phases and discontinuous phase transitions connecting them to symmetry-broken phases

Connecting the Dots: Tensor Network Algorithms for Two-Dimensional Strongly-Correlated Systems

Tensor network algorithms (TNAs) represent one of the most recent developments in the field of numerical methods for the simulation of strongly-correlated many-body systems. Arising as a natural consequence of an improved understanding of the entanglement structures intrinsic to the ground-state manifolds of many-body Hilbert spaces, they correspond to algorithms exploiting entropic constraints expected to arise in various classes of many-body ground states. In this work we apply and develop TNAs for the simulation of various strongly-correlated lattice models. Concretely, we apply tensor network renormalization (TNR) to the study of the classical Blume-Capel model (BCM). We propose to exploit the RG features specific to TNR to obtain an indicator for the vicinity of (multi-)critical points. We show that in the case of the BCM it leads to a location of its tricritical point matching the accuracy of state-of-the-art Monte Carlo approaches. This allows us to characterize the underlying $c=7/10$ conformal field theory with an excellent accuracy. We then present a self-contained introduction to the most widely used techniques for the simulation of one- and two-dimensional quantum systems, where we cover matrix product states (MPS) and projected entangled-pair states (PEPS) in detail. We briefly discuss the multi-scale entanglement renormalization Ansatz (MERA). We apply infinite PEPS (iPEPS) to the simulation of the Kitaev-Heisenberg (KH) model, proposed as an effective low-energy theory for the so-called Iridate compounds of the form $\mathrm{A_2IrO_3}$ ($\mathrm{A=Na,Li}$). We show the ability of iPEPS to accurately encode the complex ground-state physics of Kitaev's honeycomb model. When considering the KH model we confirm the existence of all previously found phases, locate all phase transitions in the phase diagram, finding good agreement with previous studies, and provide estimates for the survival regions of the spin-liquid phases in the thermodynamic limit. We briefly discuss the nature of these transitions. We conclude this work with a study of various formulations of iPEPS on cylindrical geometries. We benchmark the proposed formulations by studying the transverse-field Ising model and find good performance for a subset of the formulations studied. We then carry out a comparison between iPEPS and iMPS methods for the Heisenberg and Hubbard models and find a range of cylinder widths over which both methods exhibit comparable performance. We find evidence for the potential of iPEPS simulations on cylinders and argue that our findings provide support for future studies employing both MPS and PEPS methods in conjunction

Computational analysis of amino acids and their sidechain analogs in crowded solutions of RNA nucleobases with implications for the mRNA–protein complementarity hypothesis

Many critical processes in the cell involve direct binding between RNAs and proteins, making it imperative to fully understand the physicochemical principles behind such interactions at the atomistic level. Here, we use molecular dynamics simulations and 15 μs of sampling to study the behavior of amino acids and amino acid sidechain analogs in high-concentration aqueous solutions of standard RNA nucleobases. Structural and energetic analysis of simulated systems allows us to derive interaction propensity scales for different amino acid/nucleobase combinations. The derived scales closely match and greatly extend the available experimental data, providing a comprehensive foundation for studying RNA–protein interactions in different contexts. By using these scales, we demonstrate a statistically significant connection between nucleobase composition of human mRNA coding sequences and nucleobase interaction propensities of their cognate protein sequences. For example, pyrimidine density profiles of mRNAs match uracil-propensity profiles of their cognate proteins with a median Pearson correlation coefficient of R = −0.70. Our results provide support for the recently proposed hypotheses that mRNAs and their cognate proteins may be physicochemically complementary to each other and bind, especially if unstructured, with the complementarity level being negatively influenced by mRNA adenine content. Finally, we utilize the derived scales to refine the complementarity hypothesis and closely examine its physicochemical underpinnings.ISSN:1362-4962ISSN:0301-561