arXiv subjects

Anika Götz

Publications and source records attributed to Anika Götz.

6 recordsLinked to original sources

arXiv2026

Analytic continuation of Green's functions with a neural network

An important problem in many-body physics is to reconstruct the spectral density from the imaginary-time domain Green's function. Typically, the imaginary-time Green's function is generated by Monte Carlo methods. As the one-point fermionic kernel diverges exponentially for large frequencies, numerical noise generically causes instabilities. We use a convolutional neural network to obtain the spectral density for a given imaginary time Green's function. The network is trained by data which we generate using random Gaussians. We improve the training data set available by including collision centers for the Gaussians rather than employing uniformly distributed Gaussians. Our network is constructed in such a way that its output fulfills positive semidefiniteness. We compare the results of our network with results of the Maximum Entropy method (MaxEnt), a standard method for the same reconstruction problem for the spectral density. This comparison is performed for three different cases, namely our Gaussian based test data as well as two physical models, the 1d Hubbard model showing spin-charge separation, and the two-dimensional SSH model in the self-consistent Born approximation. We find that the network outperforms MaxEnt when presented data close to the training set. For the physical models considered, MaxEnt recognizes physical features more precisely as compared to our network prediction. While it is hard to improve MaxEnt, the quality of the network depends on the training data set which can be systematically enhanced and improved.

cond-mat.str-el↗

arXiv2025

Phases and Exotic Phase Transitions of a Two-Dimensional Su-Schrieffer-Heeger Model

We study a Su-Schrieffer-Heeger electron-phonon model on a square lattice by means of auxiliary-field quantum Monte Carlo simulations. The addition of a symmetry-allowed interaction permits analytical integration over the phonons at the expense of discrete Hubbard-Stratonovich fields with imaginary-time correlations. Using single-spin-flip and global updates, we investigate the phase diagram at the O(4)-symmetric point as a function of hopping $t$ and phonon frequency $ω_0$. For $t=0$, where electron hopping is boson assisted, the model maps onto an unconstrained $\mathbb{Z}_2$ gauge theory. A key quantity is the emergent effective flux per plaquette, which equals $π$ in the assisted-hopping regime and vanishes for large $t$. Phases in the former regime can be understood in terms of instabilities of emergent Dirac fermions. Our results support a direct and continuous transition between a $(π,0)$ valence bond solid (VBS) and an antiferromagnetic (AFM) phase with increasing $ω_0$. For large $t$ and small $ω_0$, we find finite-temperature signatures, a disordered pseudogap phase, of a previously reported $(π,π)$ VBS ground state related to a nesting instability. With increasing $ω_0$, AFM order again emerges.

cond-mat.str-el↗

arXiv2025

Hubbard and Heisenberg models on hyperbolic lattices: Metal-insulator transitions, global antiferromagnetism, and enhanced boundary fluctuations

We study the Hubbard and Heisenberg models on hyperbolic lattices with open boundary conditions by means of mean-field approximations, spin-wave theory, and quantum Monte Carlo (QMC) simulations. For the Hubbard model we use the auxiliary-field approach and for Heisenberg systems the stochastic series expansion algorithm and concentrate on bipartite lattices where the QMC simulations are free of the negative sign problem. The hyperbolic lattices have an extensive number of sites on the boundary, such that one has to distinguish between bulk and total density of states (DOS). The considered lattices are characterized by a Dirac-like total DOS, Schläfli indices $\{p,q\}=\{10,3\}$ and $\{8,3\}$, as well as by flat bands, $\{8,8\}$. The Dirac total DOS cuts off the logarithmic divergence of the staggered spin susceptibility and allows for a finite $U$ metal-to-insulator transition. This transition has the same mean-field exponents as for the Gross-Neveu transition in Euclidean space. We argue that this transition is induced by the open-boundary conditions and that it will be absent in the periodic case. In the presence of flat bands we observe the onset of magnetic ordering at any finite $U$. This conclusion holds even though the bulk DOS is constant at the Fermi energy for the three considered lattices. The magnetic state at intermediate coupling can be described as a global antiferromagnet. It breaks the $C_p$ rotational and time-reversal symmetries but remains invariant under combined $C_p \mathcal{T}$ transformations. The state is characterized by macroscopic ferromagnetic moments, that globally cancel. We observe that fluctuations on the boundary of the system are greatly enhanced: While spin-wave calculations predict the breakdown of antiferromagnetism on the boundary but not in the bulk, QMC simulations show a marked reduction of the staggered moment on the edge of the system.

cond-mat.str-el↗

arXiv2024

Tuning the order of a deconfined quantum critical point

We consider a Su-Schrieffer-Heeger model in the assisted hopping limit, where direct electron hopping is subdominant. At fixed electron-phonon coupling and in the absence of Coulomb interactions, the model shows a deconfined quantum critical point (DQCP) between a $(π,0)$ valence bond solid in the adiabatic limit and a quantum antiferromagnetic (AFM) phase at high phonon frequencies. Here, we show that by adding terms to the model that reinforce the AFM phase, thereby lowering the critical phonon frequency, the quantum phase transition becomes strongly first order. Our results do not depend on the symmetry of the model. In fact, adding a Hubbard-$U$ term to the model lowers the O(4) symmetry of the model to SU(2) such that the DQCP we observe has the same symmetries as other models that account for similar quantum phase transitions.

cond-mat.str-el↗

arXiv2023

Flat band projections: Sign problem mapping for frustrated spin systems

Projection of the Coulomb potential onto flat bands paves the way to design various interactions in the particle-hole and particle-particle channels. Here we pose the question if we can use this mapping to overcome the negative sign problem for the simplest possible frustrated spin system consisting a trimer of spins-1/2 coupled with an antiferromagnetic exchange interaction. While the answer is negative, we show that we can map the sign problem for frustrated spin systems onto a problem where we need to simulate particle-hole symmetric systems but with long-ranged Coulomb interactions prevailing over short-ranged ones. While the latter systems are currently not accessible to auxiliary field determinant quantum Monte Carlo, this mapping motivates algorithmic development that may overcome this issue.

cond-mat.str-el↗

arXiv2022

Valence-bond solid to antiferromagnet transition in the two-dimensional Su-Schrieffer-Heeger model by Langevin dynamics

The two-dimensional Su-Schrieffer-Heeger model of electrons coupled to quantum phonons is investigated using Langevin dynamics within the framework of auxiliary-field quantum Monte Carlo. Based on an explicit determination of the density of zeros of the fermion determinant, it is argued that the method is efficient in the challenging adiabatic limit. Large-scale simulations at the O(4)-symmetric point establish that the ground state of the 2D SSH model undergoes a transition from a $(π,π)$ valence bond solid to an antiferromagnet with increasing phonon frequency, yet still in the adiabatic regime. The single-particle spectrum illustrates the renormalization of the electronic band and suggests the existence of a gapped polaronic band, whereas the particle-hole channels show gapless modes associated with long-range bond and magnetic order, respectively. The simulations are supplemented with a mean-field analysis and a self-consistent Born proximation.

cond-mat.str-el↗