Publications

Order by: publication date number of citations

• The ALF (Algorithms for Lattice Fermions) project release 2.0. Documentation for the auxiliary-field quantum Monte Carlo code

  F. F. Assaad, M. Bercx, F. Goth, A. Götz, J. S. Hofmann, E. Huffman, Z. Liu, F. Parisen Toldin, J. S. E. Portela, J. Schwab

  SciPost Phys. Codebases 1 (2022) · published 22 August 2022 · licensed under CC BY-SA (4.0) | Toggle abstract · pdf

  The Algorithms for Lattice Fermions package provides a general code for the finite-temperature and projective auxiliary-field quantum Monte Carlo algorithm. The code is engineered to be able to simulate any model that can be written in terms of sums of single-body operators, of squares of single-body operators and single-body operators coupled to a bosonic field with given dynamics. The package includes five pre-defined model classes: SU(N) Kondo, SU(N) Hubbard, SU(N) t-V and SU(N) models with long range Coulomb repulsion on honeycomb, square and N-leg lattices, as well as $Z_2$ unconstrained lattice gauge theories coupled to fermionic and $Z_2$ matter. An implementation of the stochastic Maximum Entropy method is also provided. One can download the code from our Git instance at https://git.physik.uni-wuerzburg.de/ALF/ALF/-/tree/ALF-2.0 and sign in to file issues.

  47 citations

• Reduced Dynamics of Full Counting Statistics

  Felix A. Pollock, Emanuel Gull, K. Modi, Guy Cohen

  SciPost Phys. 13, 027 (2022) · published 18 August 2022 | Toggle abstract · pdf

  We present a theory of modified reduced dynamics in the presence of counting fields. Reduced dynamics techniques are useful for describing open quantum systems at long emergent timescales when the memory timescales are short. However, they can be difficult to formulate for observables spanning the system and its environment, such as those characterizing transport properties. A large variety of mixed system--environment observables, as well as their statistical properties, can be evaluated by considering counting fields. Given a numerical method able to simulate the field-modified dynamics over the memory timescale, we show that the long-lived full counting statistics can be efficiently obtained from the reduced dynamics. We demonstrate the utility of the technique by computing the long-time current in the nonequilibrium Anderson impurity model from short-time Monte Carlo simulations.

  10 citations

• Ground-state phase diagram of quantum link electrodynamics in $(2+1)$-d

  Tomohiro Hashizume, Jad C. Halimeh, Philipp Hauke, Debasish Banerjee

  SciPost Phys. 13, 017 (2022) · published 12 August 2022 | Toggle abstract · pdf

  The exploration of phase diagrams of strongly interacting gauge theories coupled to matter in lower dimensions promises the identification of exotic phases and possible new universality classes, and it facilitates a better understanding of salient phenomena in Nature, such as confinement or high-temperature superconductivity. The emerging new techniques of quantum synthetic matter experiments as well as efficient classical computational methods with matrix product states have been extremely successful in one spatial dimension, and are now motivating such studies in two spatial dimensions. In this work, we consider a $\mathrm{U}(1)$ quantum link lattice gauge theory where the gauge fields, represented by spin-$\frac{1}{2}$ operators are coupled to a single flavor of staggered fermions. Using matrix product states on infinite cylinders with increasing diameter, we conjecture its phase diagram in $(2+1)$-d. This model allows us to smoothly tune between the $\mathrm{U}(1)$ quantum link and the quantum dimer models by adjusting the strength of the fermion mass term, enabling us to connect to the well-studied phases of those models. Our study reveals a rich phase diagram with exotic phases and interesting phase transitions to a potential liquid-like phase. It thus furthers the collection of gauge theory models that may guide future quantum-simulation experiments.

  10 citations

• 2D topological matter from a boundary Green's functions perspective: Faddeev-LeVerrier algorithm implementation

  Miguel Alvarado, Alfredo Levy Yeyati

  SciPost Phys. 13, 009 (2022) · published 25 July 2022 | Toggle abstract · pdf

  Since the breakthrough of twistronics a plethora of topological phenomena in correlated systems has appeared. These devices can be typically analyzed in terms of lattice models using Green's function techniques. In this work we introduce a general method to obtain the boundary Green's function of such models taking advantage of the numerical Faddeev-LeVerrier algorithm to circumvent some analytical constraints of previous works. We illustrate our formalism analyzing the edge features of a Chern insulator, the Kitaev square lattice model for a topological superconductor and the Checkerboard lattice hosting topological flat bands. The efficiency and accuracy of the method is demonstrated by comparison to standard recursive Green's function calculations and direct diagonalizations.

  6 citations

• Entanglement entropy in quantum spin chains with broken parity number symmetry

  Arash Jafarizadeh, M. A. Rajabpour

  SciPost Phys. 12, 195 (2022) · published 14 June 2022 | Toggle abstract · pdf

  Consider a generic quantum spin chain that can be mapped to free quadratic fermions via Jordan-Wigner (JW) transformation. In the presence of arbitrary boundary magnetic fields, this Hamiltonian is no longer a quadratic Hamiltonian after JW transformation. Using ancillary sites and enlarging the Hamiltonian we first introduce a bigger quadratic Hamiltonian. Then we diagonalize this enlarged Hamiltonian in its most generic form and show that all the states are degenerate because of the presence of a zero mode. The eigenstates of the original spin chain with boundary magnetic fields can be derived after appropriate projection. We study in-depth the properties of the eigenstates of the enlarged Hamiltonian. In particular, we find: 1) the eigenstates in configuration bases, 2) calculate all the correlation functions, 3) find the reduced density matrices, 4) calculate the entanglement entropy. We show that the generic eigenstate of the enlarged Hamiltonian (including the eigenstates of the original spin chain) breaks the parity number symmetry and consequently one needs to take care of some technicalities regarding the calculation of the reduced density matrix and entanglement entropy. Interestingly we show that the entanglement structure of these eigenstates is quite universal and independent of the Hamiltonian. We support our results by applying them to a couple of examples.

  5 citations

• Real-time ab initio description of the photon-echo mechanisms in extended systems: the case study of bulk GaAs

  Marco D'Alessandro, Davide Sangalli

  SciPost Phys. 12, 193 (2022) · published 13 June 2022 | Toggle abstract · pdf

  In this paper we present an ab initio real-time analysis of free polarization decay and photon echo in extended systems. As a prototype material, we study bulk GaAs driven by ultra-short laser pulses of 10 fs (energy spread of 0.4 eV), with frequency tuned in the continuum of the optical spectrum. We compute the electronic polarization P(t), and define a computational procedure to extract the echo signal in the dipole approximation. Results are obtained in both the low and high field regime, and compared with a two-levels system (TLS) model, with parameters extracted from the ab initio simulations. ab initio results are in optimal agreement with the TLS in the low-field case, whereas some differences are observed in the high-field regime where the multi-band nature of GaAs becomes relevant. In the high field regime we compute the pulse area, and look for fluences with pulse area close to {\pi}. We highlight that such fluences are well below the damage threshold of GaAs. However a unique value of the area cannot be defined, due to the strong dependence of the transition dipoles in the energy window excited by the laser pulse.

• On the generalizability of artificial neural networks in spin models

  Hon Man Yau, Nan Su

  SciPost Phys. Core 5, 032 (2022) · published 8 June 2022 | Toggle abstract · pdf

  The applicability of artificial neural networks (ANNs) is typically limited to the models they are trained with and little is known about their generalizability, which is a pressing issue in the practical application of trained ANNs to unseen problems. Here, by using the task of identifying phase transitions in spin models, we establish a systematic generalizability such that simple ANNs trained with the two-dimensional ferromagnetic Ising model can be applied to the ferromagnetic q-state Potts model in different dimensions for q>=2. The same scheme can be applied to the highly nontrivial antiferromagnetic q-state Potts model. We demonstrate that similar results can be obtained by reducing the exponentially large state space spanned by the training data to one that comprises only three representative configurations artificially constructed through symmetry considerations. We expect our findings to simplify and accelerate the development of machine learning-assisted tasks in spin-model related disciplines in physics and materials science.

  6 citations

• Long-term memory magnetic correlations in the Hubbard model: A dynamical mean-field theory analysis

  Clemens Watzenböck, Martina Fellinger, Karsten Held, Alessandro Toschi

  SciPost Phys. 12, 184 (2022) · published 7 June 2022 | Toggle abstract · pdf

  We investigate the onset of a not-decaying asymptotic behavior of temporal magnetic correlations in the Hubbard model in infinite dimensions. This long-term memory feature of dynamical spin correlations can be precisely quantified by computing the difference between the zero-frequency limit of the Kubo susceptibility and the corresponding static isothermal one. Here, we present a procedure for reliably evaluating this difference starting from imaginary time-axis data, and apply it to the testbed case of the Mott-Hubbard metal-insulator transition (MIT). At low temperatures, we find long-term memory effects in the entire Mott regime, abruptly ending at the first order MIT. This directly reflects the underlying local moment physics and the associated degeneracy in the many-electron spectrum. At higher temperatures, a more gradual onset of an infinitely-long time-decay of magnetic correlations occurs in the crossover regime, not too far from the Widom line emerging from the critical point of the MIT. Our work has relevant algorithmic implications for the analytical continuation of dynamical susceptibilities in strongly correlated regimes and offers a new perspective for unveiling fundamental properties of the many-particle spectrum of the problem under scrutiny.

  15 citations

• Stripes in the extended $t-t^\prime$ Hubbard model: A Variational Monte Carlo analysis

  Vito Marino, Federico Becca, Luca F. Tocchio

  SciPost Phys. 12, 180 (2022) · published 1 June 2022 | Toggle abstract · pdf

  By using variational quantum Monte Carlo techniques, we investigate the instauration of stripes (i.e., charge and spin inhomogeneities) in the Hubbard model on the square lattice at hole doping $\delta=1/8$, with both nearest- ($t$) and next-nearest-neighbor hopping ($t^\prime$). Stripes with different wavelengths $\lambda$ (denoting the periodicity of the charge inhomogeneity) and character (bond- or site-centered) are stabilized for sufficiently large values of the electron-electron interaction $U/t$. The general trend is that $\lambda$ increases going from negative to positive values of $t^\prime/t$ and decreases by increasing $U/t$. In particular, the $\lambda=8$ stripe obtained for $t^\prime=0$ and $U/t=8$ [L.F. Tocchio, A. Montorsi, and F. Becca, SciPost Phys. 7, 21 (2019)] shrinks to $\lambda=6$ for $U/t\gtrsim 10$. For $t^\prime/t<0$, the stripe with $\lambda=5$ is found to be remarkably stable, while for $t^\prime/t>0$, stripes with wavelength $\lambda=12$ and $\lambda=16$ are also obtained. In all these cases, pair-pair correlations are highly suppressed with respect to the uniform state (obtained for large values of $|t^\prime/t|$), suggesting that striped states are not superconducting at $\delta=1/8$.

  12 citations

• Critical properties of quantum three- and four-state Potts models with boundaries polarized along the transverse field

  Natalia Chepiga

  SciPost Phys. Core 5, 031 (2022) · published 30 May 2022 | Toggle abstract · pdf

  By computing the low-lying energy excitation spectra with the density matrix renormalization group algorithm we show that boundaries polarized in the direction of the transverse field lead to scale-invariant conformal towers of states at the critical point of the quantum four-state Potts model - a special symmetric case of the Ashkin-Teller model. Furthermore, by direct comparison of the excitation spectra we phenomenologically establish the duality between the transverse-polarized and three-state-mixed boundary conditions at the four-state Potts critical point. Finally, for completeness, we verify that in the quantum three-state Potts model the "new" boundary conditions dual to the mixed ones can be realized by polarizing edge spins along the transverse field.

  7 citations