Session D48: Quantum Many-Body Systems and Methods I

Correlated Electron Dynamics in Finite Hubbard Clusters: Benchmarking the G1–G2 Scheme

The selfconsistent theoretical treatment of correlation and quantum effects beyond one-dimensional systems is a particular challenge that has been successfully attacked with nonequilibrium Green functions (NEGF) methods [1]. However, NEGF simulations are hampered by a cubic scaling of the computation time with the number of time steps N_t. Recently, a dramatic acceleration has been achieved within the G1–G2 scheme [2] by transforming the NEGF equations, within the Hartree-Fock GKBA, to a time local form for the single-particle and two-particle Green functions. A detailed discussion of the method, its application to a variety of selfenergies including particle-particle and particle-hole T-matrix approximation, GW approximation, and dynamically screened ladder approximation was presented recently [3]. Here, we present extensive tests of the G1–G2 scheme within the screened ladder approximation for finite Hubbard clusters out of equilibrium. Stable simulations over long times are achieved by enforcing contraction consistency and by performing a purification of the dynamics [4].

[1] N. Schlünzen et al., PRB 93, 035107 (2016)

[2] N. Schlünzen et al., PRL 124, 076601 (2020)

[3] J.-P. Joost et al., PRB 101, 245101 (2020)

[4] F. Lackner et al., PRA 91, 023412 (2015)   

Magnetism and Mottness in the unfrustrated triangular lattice Hubbard model: a cellular dynamical mean-field study

We investigate the phase diagram of the unfrustrated triangular lattice Hubbard model in a center-focused cellular dynamical mean-field theory (CDMFT) approach using impurity clusters of 4, 7 and 19 sites [1,2]. We investigate the Mott metal-to-insulator transition and crossover region in terms of these cluster sizes. Using a magnetic symmetry-broken approach of the CDMFT, allowing for a rotations of spins on the Bloch sphere, we are able to investigate the magnetic ordering of the different cluster schemes.   

Precise ground state of multi-orbital Mott systems via the variational discrete action theory

Determining the ground state of multi-orbital Hubbard models is critical for understanding strongly correlated electron materials, yet existing methods struggle to reach zero temperature and infinite system size simultaneously. Even in infinite dimensions, the solution via the dynamical mean-field theory (DMFT) is limited by the absence of unbiased impurity solvers for zero temperature and multiple orbitals. The recently developed variational discrete action theory (VDAT) offers a new approach, with a variational ansatz that is controlled by an integer \mathcal{N}, and monotonically approaches the exact solution at an exponentially increasing computational cost. Here we implement VDAT for the multi-orbital Hubbard model in d=\infty for \mathcal{N}=2-4. At \mathcal{N}=2, VDAT rigorously recovers the multi-orbital Gutzwiller approximation, reproducing known results. At \mathcal{N}=3, VDAT qualitatively and quantitatively captures the competition between U, J, and the crystal field in the two-band Hubbard model, with a negligible computational cost. VDAT will have far-ranging implications for understanding strongly correlated materials.   

Non-local correlations and criticality in the triangular lattice Hubbard model

We investigate the role of non-local electronic correlations at finite temperatures in the half-filled triangular lattice Hubbard model using the dynamical vertex approximation (DΓA), a diagrammatic extension [1] of the dynamical mean-field theory (DMFT). We analyze the impact of (quantum) phase transitions on finite temperature properties at the one- and two-particle level. We discuss the absence of magnetic ordering at finite temperatures due to the fulfilment of the Mermin-Wagner theorem and the (Mott) metal-insulator crossover. In addition we compare the results of this method to the ones obtained by other cutting-edge techniques like DMFT, its real-space cluster extension cellular dynamical mean-field theory (CDMFT) and diagrammatic Monte Carlo (DiagMC) [2].   

The Mott metal-insulator transition in the two-dimensional Hubbard model - a cellular dynamical mean-field study on large clusters

We study the half-filled two-dimensional Hubbard model on a square lattice in cellular dynamical mean-field theory (CDMFT), a real-space cluster extension [1] of the dynamical mean-field theory. By increasing the number of cluster sites up to 6x6 we observe a progressive reduction of the onset interaction U* of a metal-insulator crossover. In particular, in the case of 4x4 sites, we observe a site-dependent U, which is lower at the center sites is lower than at the corner sites. In addition to this real-space analysis we investigate different periodization schemes for the one-particle spectral function and argue that a center-focused [2] cumulant scheme is well-suited in the intermediate coupling regime of U due to its locality.   

Controlled bond expansion for DMRG ground state search at single-site costs

We present a controlled bond expansion (CBE) approach for ground state searches based on the density matrix renormalization group (DMRG) employing matrix product states (MPS). The main idea of CBE-DMRG is as follows: Before optimizing the center tensor of an MPS in the site canonical form, the isometry on the next site is expanded by the most important contributions of its orthogonal complement. These contributions are determined by considering how the Hamiltonian acts on the current state. The accuracy of CBE-DMRG is comparable to two-site DMRG, but its numerical costs scale like those of one-site DMRG. Moreover, in contrast to previous one-site methods involving bond expansion, it does not rely on any ad-hoc mixing parameters. Starting from an initial state with low bond-dimension, the CBE prescription for increasing the bond dimension is controlled, automated and more economical than the manual adjustment typically used for two-site DMRG, leading to an additional significant speedup for reaching convergence. We illustrate the numerical performance of CBE-DMRG with several examples of fermionic models, including free fermions on a chain for benchmarking and a Kondo lattice on a cylinder as a challenging application.   

Computing Spectral functions of strongly correlated Hamiltonians using DMRG: root-N Krylov space approach for correction-vectors

We propose a method to compute spectral functions of generic Hamiltonians using the density matrix renormalization group (DMRG) method directly in frequency space, based on a modified Krylov space approach to compute the correction-vectors. The approach entails the calculation of the root-N (N = 2 is the standard square root) of the Hamiltonian propagator using Krylov space decomposition, and repeating this procedure N times to obtain the actual correction-vector. Even though the approach still involves separate calculations for different target frequencies, we show that it greatly alleviates the burden of keeping a large bond dimension as in the standard correction-vector DMRG method, while achieving better computational performance at large N. Finally, we apply this approach to spin and charge spectral functions of t-J and Hubbard models in the challenging two-leg ladder geometry, showing that it also reaches a much improved resolution at large frequencies.   

Energy twisted boundary condition

Thermal transport in condensed matter systems is traditionally formulated as a response to a background gravitational field. In this work, we seek a twisted boundary condition formalism for thermal transport in analog to the U(1) twisted boundary condition for electrical transport. We started by implementing the energy twisted boundary condition in CFT. Then using the transfer matrix method, we obtained the thermal Meissner stiffness of the Ising model and disordered Fermion model with energy twisted boundary condition. We also identified boost deformation for integrable systems as a similar formalism as energy twisted boundary condition and computed linear and nonlinear Drude weight for XXZ model.    

Interplay of spin-orbit coupling and non-local correlations with the Two-Particle Self-Consistent method

We show in which way it is possible to include spin-orbit coupling (SOC) terms in the Two-Particle Self-Consistent method (TPSC). TPSC is a many-body method, valid for weak to intermediate interaction strength, which with moderate computational effort allows to investigate non-local correlation effects [Vilk, Tremblay J. Phys. I France, 7 11 (1997) 1309-1368]. Originally developed for single-band lattice models, in recent years TPSC was extended to the multi-orbital case [Zantout et al., Phys. Rev. Lett. 123, 256401 (2019), Zantout et al., Annalen der Physik 2000399 (2021)]. Inclusion of SOC into TPSC is desirable to study systems in which the effects of SOC cannot be neglected as e.g. in Sr2RuO4 [Phys. Rev. Lett. 101, 026406 (2008)]. However, including SOC into TPSC is not straightforward since TPSC in its original formulation relies on spin rotational symmetry, a symmetry which is explicitly broken by SOC terms. We present key ideas which make this nevertheless possible and discuss the effect spin-orbit coupling on the self-energy and spin and charge correlation functions of interacting model systems.    

Entanglement Entropy from Nonequilibrium Work

The Rényi entanglement entropy in quantum many-body systems can be viewed as the difference in free energy between partition functions with different trace topologies. We introduce an external field λ that controls the partition function topology, allowing us to define a notion of nonequilibrium work as λ is varied smoothly. Nonequilibrium fluctuation theorems of the work provide us with statistically exact estimates of the Rényi entanglement entropy.  We use these ideas to extract universal information from quantum Monte Carlo simulations of spin models in one and two dimensions. The vast gain in efficiency of this method allows us to access unprecedented system sizes up to 192×96 spins for the square lattice Heisenberg antiferromagnet.   

Rainbow Scars: From Area to Volume Law

Quantum many-body scars(QMBS) constitute a new quantum dynamical regime in which rare "scarred" eigenstates mediate weak ergodicity breaking. One open question is to understand the most general setting in which these states arise. In this work, we develop a generic construction that embeds a new class of QMBS, rainbow scars, into the spectrum of an arbitrary Hamiltonian. Unlike other examples of QMBS, rainbow scars display extensive bipartite entanglement entropy while retaining a simple entanglement structure. Specifically, the entanglement scaling is volume-law for a random bipartition, while scaling for a fine-tuned bipartition is sub-extensive. When internal symmetries are present, the construction leads to multiple, and even towers of rainbow scars revealed through distinctive non-thermal dynamics. To this end, we provide an experimental road map for realizing rainbow scar states in a Rydberg-atom quantum simulator, leading to coherent oscillations distinct from the strictly sub-volume-law QMBS previously realized in the same system.   

Interactions and phonons derived from first principles using quantum Monte Carlo techniques

There are many systems which possess strong interactions and lattice degrees of freedom including high-temperature superconductors [1] and color centers in semiconductors [2]. However, electron-phonon models are typically derived within the framework of band structure, which leads to double-counting issues when interactions are re-introduced, among other issues of accuracy.

 

We investigate a new approach to deriving models that inherently includes one-body, two-body, and lattice terms from first principles quantum Monte Carlo (QMC) calculations [3]. This approach is based on scalable correlated electron calculations, and it offers high accuracy while avoiding double-counting. We assess this QMC downfolding approach on a series of well-characterized small molecules, comparing the spectra and Franck-Condon factors against the equation of motion coupled cluster method and experiments.

 

[1] Z.-X. Shen, et. al., Philos. Mag. B 82 1349-1368 (2002).

[2] M. Bockstedte, et. al., npj Quant. Mater. 3 31 (2018).

[3] H. Zheng, et. al., Front. Phys. 6 43 (2018).   

Electronic excitations in correlated finite 2D materials generated by ion impact

The impact of ions on solid targets is of high interest in many fields and has been extensively treated in linear response. However, ions give rise to a very strong, highly localized and fast excitation that my well lead to nonlinear and nonadiabatic effects. The ion-initiated dynamics are particularly interesting in strongly correlated materials giving rise to nontrivial electronic processes such as the excitation of doublons [1]. We present a time-resolved analysis of these processes in finite 2D graphene-type clusters, using a

nonequilibrium Green functions (NEGF) approach. While NEGF can handle any dimensionality and geometry, however, they are computationally costly (cubic scaling with the simulation duration T).  Recently, we could achieve linear scaling with T by introducing the G1-G2 scheme [2]. It has allowed us to perform long simulations and, in addition, to include higher order electronic selfenergies accounting for strong coupling and dynamical screening. We use this to explore the doublon generation by multiple ion impacts [3] and the charge transfer between target and projectile [4].  

[1] K. Balzer et al., Phys. Rev. Lett. 121, 267602 (2018)

[2] N. Schluenzen et al., Phys. Rev. Lett. 124, 076601 (2020)

[3] L. Borkowski et al., phys. stat. sol. (b)  (2021), arXiv:2110.06644

[4] K. Balzer and M. Bonitz, Contrib. Plasma Phys. e202100041 (2021)