Publications

Order by: publication date number of citations

• HYPERTILING — a high performance Python library for the generation and visualization of hyperbolic lattices

  Manuel Schrauth, Yanick Thurn, Florian Goth, Jefferson S. E. Portela, Dietmar Herdt, Felix Dusel

  SciPost Phys. Codebases 34 (2024) · published 28 August 2024 | Toggle abstract · pdf

  HYPERTILING is a high-performance Python library for the generation and visualization of regular hyperbolic lattices embedded in the Poincar\'e disk model. Using highly optimized, efficient algorithms, hyperbolic tilings with millions of vertices can be created in a matter of minutes on a single workstation computer. Facilities including computation of adjacent vertices, dynamic lattice manipulation, refinements, as well as powerful plotting and animation capabilities are provided to support advanced uses of hyperbolic graphs. In this manuscript, we present a comprehensive exploration of the package, encompassing its mathematical foundations, usage examples, applications, and a detailed description of its implementation.

  5 citations

• Density-matrix mean-field theory

  Junyi Zhang, Zhengqian Cheng

  SciPost Phys. 17, 062 (2024) · published 23 August 2024 | Toggle abstract · pdf

  Mean-field theories have proven to be efficient tools for exploring diverse phases of matter, complementing alternative methods that are more precise but also more computationally demanding. Conventional mean-field theories often fall short in capturing quantum fluctuations, which restricts their applicability to systems with significant quantum effects. In this article, we propose an improved mean-field theory, density-matrix mean-field theory (DMMFT). DMMFT constructs effective Hamiltonians, incorporating quantum environments shaped by entanglements, quantified by the reduced density matrices. Therefore, it offers a systematic and unbiased approach to account for the effects of fluctuations and entanglements in quantum ordered phases. As demonstrative examples, we show that DMMFT can not only quantitatively evaluate the renormalization of order parameters induced by quantum fluctuations, but can also detect the topological quantum phases. Additionally, we discuss the extensions of DMMFT for systems at finite temperatures and those with disorders. Our work provides an efficient approach to explore phases exhibiting unconventional quantum orders, which can be particularly beneficial for investigating frustrated spin systems in high spatial dimensions.

• Quantum-critical properties of the one- and two-dimensional random transverse-field Ising model from large-scale quantum Monte Carlo simulations

  Calvin Krämer, Jan Alexander Koziol, Anja Langheld, Max Hörmann, Kai Phillip Schmidt

  SciPost Phys. 17, 061 (2024) · published 23 August 2024 | Toggle abstract · pdf

  We study the ferromagnetic transverse-field Ising model with quenched disorder at $T = 0$ in one and two dimensions by means of stochastic series expansion quantum Monte Carlo simulations using a rigorous zero-temperature scheme. Using a sample-replication method and averaged Binder ratios, we determine the critical shift and width exponents $\nu_\mathrm{s}$ and $\nu_\mathrm{w}$ as well as unbiased critical points by finite-size scaling. Further, scaling of the disorder-averaged magnetisation at the critical point is used to determine the order-parameter critical exponent $\beta$ and the critical exponent $\nu_{\mathrm{av}}$ of the average correlation length. The dynamic scaling in the Griffiths phase is investigated by measuring the local susceptibility in the disordered phase and the dynamic exponent $z'$ is extracted. By applying various finite-size scaling protocols, we provide an extensive and comprehensive comparison between the different approaches on equal footing. The emphasis on effective zero-temperature simulations resolves several inconsistencies in existing literature.

  4 citations

• Gaussian state approximation of quantum many-body scars

  Wouter Buijsman, Yevgeny Bar Lev

  SciPost Phys. 17, 055 (2024) · published 15 August 2024 | Toggle abstract · pdf

  Quantum many-body scars are atypical, highly nonthermal eigenstates embedded in a sea of thermal eigenstates that have been observed in, for example, kinetically constrained quantum many-body models. These special eigenstates are characterized by a bipartite entanglement entropy that scales as most logarithmically with the subsystem size. We use numerical optimization techniques to investigate if quantum many-body scars of the experimentally relevant PXP model can be well approximated by Gaussian states. Gaussian states are described by a number of parameters that scales quadratically with system size, thereby having a much lower complexity than generic quantum many-body states, for which this number scales exponentially. We find that while quantum many-body scars can typically be well approximated by (symmetrized) Gaussian states, this is not the case for ergodic (thermal) eigenstates. This observation suggests that the non-ergodic part of the PXP Hamiltonian is related to certain quadratic parent Hamiltonians, thereby hinting on the origin of the quantum many-body scars.

• Quantum robustness of the toric code in a parallel field on the honeycomb and triangular lattice

  Viktor Kott, Matthias Mühlhauser, Jan Alexander Koziol, Kai Phillip Schmidt

  SciPost Phys. 17, 053 (2024) · published 15 August 2024 | Toggle abstract · pdf

  We investigate the quantum robustness of the topological order in the toric code on the honeycomb lattice in the presence of a uniform parallel field. For a field in $z$-direction, the low-energy physics is in the flux-free sector and can be mapped to the transverse-field Ising model on the honeycomb lattice. One finds a second-order quantum phase transition in the 3D Ising$^\star$ universality class for both signs of the field. The same is true for a postive field in $x$-direction where an analogue mapping in the charge-free sector yields a ferromagnetic transverse-field Ising model on the triangular lattice and the phase transition is still 3D Ising$^\star$. In contrast, for negative $x$-field, the charge-free sector is mapped to the highly frustrated antiferromagnetic transverse-field Ising model on the triangular lattice which is known to host a quantum phase transition in the 3D XY$^\star$ universality class. Further, the charge-free sector does not always contain the low-energy physics for negative $x$-fields and a first-order phase transition to the polarized phase in the charge-full sector takes place at larger negative field values. We quantify the location of this transition by comparing quantum Monte Carlo simulations and high-field series expansions. The full extension of the topological phase in the presence of $x$- and $z$-fields is determined by perturbative linked-cluster expansions using a full graph decomposition. Extrapolating the high-order series of the charge and the flux gap allows to estimate critical exponents of the gap closing. This analysis indicates that the topological order breaks down by critical lines of 3D Ising$^\star$ and 3D XY$^\star$ type with interesting potential multi-critical crossing points. All findings for the toric code on the honeycomb lattice can be transferred exactly to the toric code on the triangular lattice.

  1 citation

• Numerical signatures of ultra-local criticality in a one dimensional Kondo lattice model

  Alexander Nikolaenko, Ya-Hui Zhang

  SciPost Phys. 17, 034 (2024) · published 5 August 2024 | Toggle abstract · pdf

  Heavy fermion criticality has been a long-standing problem in condensed matter physics. Here we study a one-dimensional Kondo lattice model through numerical simulation and observe signatures of local criticality. We vary the Kondo coupling $J_K$ at fixed doping x. At large positive $J_K$, we confirm the expected conventional Luttinger liquid phase with $2k_F=\frac{1+x}{2}$ (in units of $2\pi$), an analogue of the heavy Fermi liquid (HFL) in the higher dimension. In the $J_K ≤ 0$ side, our simulation finds the existence of a fractional Luttinger liquid (LL$\star$) phase with $2k_F=\frac{x}{2}$, accompanied by a gapless spin mode originating from localized spin moments, which serves as an analogue of the fractional Fermi liquid (FL$\star$) phase in higher dimensions. The LL$\star$ phase becomes unstable and transitions to a spin-gapped Luther-Emery (LE) liquid phase at small positive $J_K$. Then we mainly focus on the "critical regime" between the LE phase and the LL phase. Approaching the critical point from the spin-gapped LE phase, we often find that the spin gap vanishes continuously, while the spin-spin correlation length in real space stays finite and small. For a certain range of doping, in a point (or narrow region) of $J_K$, the dynamical spin structure factor obtained through the time-evolving block decimation (TEBD) simulation shows dispersion-less spin fluctuations in a finite range of momentum space above a small energy scale (around $0.035 J$) that is limited by the TEBD accuracy. All of these results are unexpected for a regular gapless phase (or critical point) described by conformal field theory (CFT). Instead, they are more consistent with exotic ultra-local criticality with an infinite dynamical exponent $z=+$. The numerical discovery here may have important implications on our general theoretical understanding of the strange metals in heavy fermion systems. Lastly, we propose to simulate the model in a bilayer optical lattice with a potential difference.

  1 citation

• LiHoF4 as a spin-half non-standard quantum Ising system

  Tomer Dollberg, Moshe Schechter

  SciPost Phys. 17, 028 (2024) · published 31 July 2024 | Toggle abstract · pdf

  LiHoF$_{4}$ is a magnetic material known for its Ising-type anisotropy, making it a model system for studying quantum magnetism. However, the theoretical description of LiHoF$_{4}$ using the quantum Ising model has shown discrepancies in its phase diagram, particularly in the regime dominated by thermal fluctuations. In this study, we investigate the role of off-diagonal dipolar terms in LiHoF$_{4}$, previously neglected, in determining its properties. We analytically derive the low-energy effective Hamiltonian of LiHoF$_{4}$, including the off-diagonal dipolar terms perturbatively, both in the absence and presence of a transverse field. Our results encompass the full \boldmath{$B_{x}-T$} phase diagram, confirming the significance of the off-diagonal dipolar terms in reducing the zero-field critical temperature and determining the critical temperature's dependence on the transverse field. We also highlight the sensitivity of this mechanism to the crystal structure by comparing our calculations with the Fe$_{8}$ system.

  1 citation

• Quantum state preparation of topological chiral spin liquids via Floquet engineering

  Matthieu Mambrini, Didier Poilblanc

  SciPost Phys. 17, 011 (2024) · published 11 July 2024 | Toggle abstract · pdf

  In condensed matter, Chiral Spin Liquids (CSL) are quantum spin analogs of electronic Fractional Quantum Hall states (in the continuum) or Fractional Chern Insulators (on the lattice). As the latter, CSL are remarkable states of matter, exhibiting topological order and chiral edge modes. Preparing CSL on quantum simulators like cold atom platforms is still an open challenge. Here we propose a simple setup on a finite cluster of spin-1/2 located at the sites of a square lattice. Using a Resonating Valence Bond (RVB) non-chiral spin liquid as initial state on which fast time-modulations of strong nearest-neighbor Heisenberg couplings are applied, following different protocols (out-of-equilibrium quench or semi-adiabatic ramping of the drive), we show the slow emergence of such a CSL phase. An effective Floquet dynamics, obtained from a high-frequency Magnus expansion of the drive Hamiltonian, provides a very accurate and simple framework fully capturing the out-of-equilibrium dynamics. An analysis of the resulting prepared states in term of Projected Entangled Pair states gives further insights on the topological nature of the chiral phase. Finally, we discuss possible applications to quantum computing.

  3 citations

• Extracting subleading corrections in entanglement entropy at quantum phase transitions

  Menghan Song, Jiarui Zhao, Zi Yang Meng, Cenke Xu, Meng Cheng

  SciPost Phys. 17, 010 (2024) · published 11 July 2024 | Toggle abstract · pdf

  We systematically investigate the finite size scaling behavior of the Rényi entanglement entropy (EE) of several representative 2d quantum many-body systems between a subregion and its complement, with smooth boundaries as well as boundaries with corners. In order to reveal the subleading correction, we investigate the quantity "subtracted EE" $S^s(l) = S(2l) - 2S(l)$ for each model, which is designed to cancel out the leading perimeter law. We find that (1) for a spin-1/2 model on a 2d square lattice whose ground state is the Neel order, the coefficient of the logarithmic correction to the perimeter law is consistent with the prediction based on the Goldstone modes; (2) for the $(2+1)d$ O(3) Wilson-Fisher quantum critical point (QCP), realized with the bilayer antiferromagnetic Heisenberg model, a logarithmic subleading correction exists when there is sharp corner of the subregion, but for subregion with a smooth boundary our data suggests the absence of the logarithmic correction to the best of our efforts; (3) for the $(2+1)d$ SU(2) J-Q$_2$ and J-Q$_3$ model for the deconfined quantum critical point (DQCP), we find a logarithmic correction for the EE even with smooth boundary.

  21 citations

• THz higher-order topological photonics in Ge-on-Si heterostructures

  Ian Colombo, Pietro Minazzi, Emiliano Bonera, Fabio Pezzoli, Jacopo Pedrini

  SciPost Phys. Core 7, 039 (2024) · published 4 July 2024 | Toggle abstract · pdf

  We design germanium-based higher-order topological cavities for terahertz applications by breaking the symmetry of a two-dimensional photonic crystal following the Su-Schrieffer-Heeger model. Calculations demonstrate the parity inversion of the electric field in differently deformed unit cells. The interface between domains of opposite topology presents edge and corner modes. The former are chiral, locking light propagation to its helicity. The latter prove that Ge-based structures can be used as high-order topological photonic crystals. These findings can accelerate the development of Si-photonic components working in a spectral range of high technological interest.