Antiferromagnetic Bosonic t-J Models and Their Quantum Simulation in Tweezer Arrays.

The combination of optical tweezer arrays with strong interactions-via dipole exchange of molecules and Van der Waals interactions of Rydberg atoms-has opened the door for the exploration of a wide variety of quantum spin models. A next significant step will be the combination of such settings with mobile dopants. This will enable one to simulate the physics believed to underlie many strongly correlated quantum materials. Here, we propose an experimental scheme to realize bosonic t-J models via encoding the local Hilbert space in a set of three internal atomic or molecular states. By engineering antiferromagnetic (AFM) couplings between spins, competition between charge motion and magnetic order similar to that in high-T_{c} cuprates can be realized. Since the ground states of the 2D bosonic AFM t-J model we propose to realize have not been studied extensively before, we start by analyzing the case of two dopants-the simplest instance in which their bosonic statistics plays a role-and compare our results to the fermionic case. We perform large-scale density matrix renormalization group calculations on six-legged cylinders, and find a strong tendency for bosonic holes to form stripes. This demonstrates that bosonic, AFM t-J models may contain similar physics as the collective phases in strongly correlated electrons.

Coexistence of superconductivity with partially filled stripes in the Hubbard model.

The Hubbard model is an iconic model in quantum many-body physics and has been intensely studied, especially since the discovery of high-temperature cuprate superconductors. Combining the complementary capabilities of two computational methods, we found superconductivity in both the electron- and hole-doped regimes of the two-dimensional Hubbard model with next-nearest-neighbor hopping. In the electron-doped regime, superconductivity was weaker and was accompanied by antiferromagnetic Néel correlations at low doping. The strong superconductivity on the hole-doped side coexisted with stripe order, which persisted into the overdoped region with weaker hole-density modulation. These stripe orders varied in fillings between 0.6 and 0.8. Our results suggest the applicability of the Hubbard model with next-nearest hopping for describing cuprate high-transition temperature (Tc) superconductivity.

Stochastic Adaptive Single-Site Time-Dependent Variational Principle.

In recent years, the time-dependent variational principle (TDVP) method based on the matrix product state (MPS) wave function formulation has shown its great power in performing large-scale quantum dynamics simulations for realistic chemical systems with strong electron-vibration interactions. In this work, we propose a stochastic adaptive single-site TDVP (SA-1TDVP) scheme to evolve the bond-dimension adaptively, which can integrate the traditional advantages of both the high efficiency of the single-site TDVP (1TDVP) variant and the high accuracy of the two-site TDVP (2TDVP) variant. Based on the assumption that the level statistics of entanglement Hamiltonians, which originate from the reduced density matrices of the MPS method, follows a Poisson or Wigner distribution, as generically predicted by random-matrix theory, additional random singular values are generated to expand the bond-dimension automatically. Tests on simulating the vibrationally resolved quantum dynamics and absorption spectra in the pyrazine molecule and perylene bisimide (PBI) J-aggregate trimer as well as a spin-1/2 Heisenberg chain show that it can be automatic and as accurate as 2TDVP but reduce the computational time remarkably.

Confinement and Mott Transitions of Dynamical Charges in One-Dimensional Lattice Gauge Theories.

Confinement is an ubiquitous phenomenon when matter couples to gauge fields, which manifests itself in a linear string potential between two static charges. Although gauge fields can be integrated out in one dimension, they can mediate nonlocal interactions which in turn influence the paradigmatic Luttinger liquid properties. However, when the charges become dynamical and their densities finite, understanding confinement becomes challenging. Here we show that confinement in 1D Z_{2} lattice gauge theories, with dynamical matter fields and arbitrary densities, is related to translational symmetry breaking in a nonlocal basis. The exact transformation to this string-length basis leads us to an exact mapping of Luttinger parameters reminiscent of a Luther-Emery rescaling. We include the effects of local, but beyond contact, interactions between the matter particles, and show that confined mesons can form a Mott-insulating state when the deconfined charges cannot. While the transition to the Mott state cannot be detected in the Green's function of the charges, we show that the metallic state is characterized by hidden off-diagonal quasi-long-range order. Our predictions provide new insights to the physics of confinement of dynamical charges, and can be experimentally addressed in Rydberg-dressed quantum gases in optical lattices.

Quantum dynamics simulation of intramolecular singlet fission in covalently linked tetracene dimer.

In this work, we study singlet fission in tetracene para-dimers, covalently linked by a phenyl group. In contrast to most previous studies, we account for the full quantum dynamics of the combined excitonic and vibrational system. For our simulations, we choose a numerically unbiased representation of the molecule's wave function, enabling us to compare with experiments, exhibiting good agreement. Having access to the full wave function allows us to study in detail the post-quench dynamics of the excitons. Here, one of our main findings is the identification of a time scale t0 ≈ 35 fs dominated by coherent dynamics. It is within this time scale that the larger fraction of the singlet fission yield is generated. We also report on a reduced number of phononic modes that play a crucial role in the energy transfer between excitonic and vibrational systems. Notably, the oscillation frequency of these modes coincides with the observed electronic coherence time t0. We extend our investigations by also studying the dependency of the dynamics on the excitonic energy levels that, for instance, can be experimentally tuned by means of the solvent polarity. Here, our findings indicate that the singlet fission yield can be doubled, while the electronic coherence time t0 is mainly unaffected.

Probing the Hall Voltage in Synthetic Quantum Systems.

In the context of experimental advances in the realization of artificial magnetic fields in quantum gases, we discuss feasible schemes to extend measurements of the Hall polarization to a study of the Hall voltage, allowing for direct comparison with solid state systems. Specifically, for the paradigmatic example of interacting flux ladders, we report on characteristic zero crossings and a remarkable robustness of the Hall voltage with respect to interaction strengths, particle fillings, and ladder geometries, which is unobservable in the Hall polarization. Moreover, we investigate the site-resolved Hall response in spatially inhomogeneous quantum phases.

Concept of Orbital Entanglement and Correlation in Quantum Chemistry.

A recent development in quantum chemistry has established the quantum mutual information between orbitals as a major descriptor of electronic structure. This has already facilitated remarkable improvements in numerical methods and may lead to a more comprehensive foundation for chemical bonding theory. Building on this promising development, our work provides a refined discussion of quantum information theoretical concepts by introducing the physical correlation and its separation into classical and quantum parts as distinctive quantifiers of electronic structure. In particular, we succeed in quantifying the entanglement. Intriguingly, our results for different molecules reveal that the total correlation between orbitals is mainly classical, raising questions about the general significance of entanglement in chemical bonding. Our work also shows that implementing the fundamental particle number superselection rule, so far not accounted for in quantum chemistry, removes a major part of correlation and entanglement seen previously. In that respect, realizing quantum information processing tasks with molecular systems might be more challenging than anticipated.

Sr_{2}MoO_{4} and Sr_{2}RuO_{4}: Disentangling the Roles of Hund's and van Hove Physics.

Sr_{2}MoO_{4} is isostructural to the unconventional superconductor Sr_{2}RuO_{4} but with two electrons instead of two holes in the Mo/Ru-t_{2g} orbitals. Both materials are Hund's metals, but while Sr_{2}RuO_{4} has a van Hove singularity in close proximity to the Fermi surface, the van Hove singularity of Sr_{2}MoO_{4} is far from the Fermi surface. By using density functional plus dynamical mean-field theory, we determine the relative influence of van Hove and Hund's metal physics on the correlation properties. We show that theoretically predicted signatures of Hund's metal physics occur on the occupied side of the electronic spectrum of Sr_{2}MoO_{4}, identifying Sr_{2}MoO_{4} as an ideal candidate system for a direct experimental confirmation of the theoretical concept of Hund's metals via photoemission spectroscopy.

Time-dependent density matrix renormalization group quantum dynamics for realistic chemical systems.

Electronic and/or vibronic coherence has been found by recent ultrafast spectroscopy experiments in many chemical, biological, and material systems. This indicates that there are strong and complicated interactions between electronic states and vibration modes in realistic chemical systems. Therefore, simulations of quantum dynamics with a large number of electronic and vibrational degrees of freedom are highly desirable. Due to the efficient compression and localized representation of quantum states in the matrix-product state (MPS) formulation, time-evolution methods based on the MPS framework, which we summarily refer to as tDMRG (time-dependent density-matrix renormalization group) methods, are considered to be promising candidates to study the quantum dynamics of realistic chemical systems. In this work, we benchmark the performances of four different tDMRG methods, including global Taylor, global Krylov, and local one-site and two-site time-dependent variational principles (1TDVP and 2TDVP), with a comparison to multiconfiguration time-dependent Hartree and experimental results. Two typical chemical systems of internal conversion and singlet fission are investigated: one containing strong and high-order local and nonlocal electron-vibration couplings and the other exhibiting a continuous phonon bath. The comparison shows that the tDMRG methods (particularly, the 2TDVP method) can describe the full quantum dynamics in large chemical systems accurately and efficiently. Several key parameters in the tDMRG calculation including the truncation error threshold, time interval, and ordering of local sites were also investigated to strike the balance between efficiency and accuracy of results.

Density-Matrix Embedding Theory Study of the One-Dimensional Hubbard-Holstein Model.

We present a density-matrix embedding theory (DMET) study of the one-dimensional Hubbard-Holstein model, which is paradigmatic for the interplay of electron-electron and electron-phonon interactions. Analyzing the single-particle excitation gap, we find a direct Peierls insulator to Mott insulator phase transition in the adiabatic regime of slow phonons in contrast to a rather large intervening metallic phase in the anti-adiabatic regime of fast phonons. We benchmark the DMET results for both on-site energies and excitation gaps against density-matrix renormalization group (DMRG) results and find good agreement of the resulting phase boundaries. We also compare the full quantum treatment of phonons against the standard Born-Oppenheimer (BO) approximation. The BO approximation gives qualitatively similar results to DMET in the adiabatic regime but fails entirely in the anti-adiabatic regime, where BO predicts a sharp direct transition from Mott to Peierls insulator, whereas DMET correctly shows a large intervening metallic phase. This highlights the importance of quantum fluctuations in the phononic degrees of freedom for metallicity in the one-dimensional Hubbard-Holstein model.

Doped Kondo chain, a heavy Luttinger liquid.

The doped 1D Kondo Lattice describes complex competition between itinerant and magnetic ordering. The numerically computed wave vector-dependent charge and spin susceptibilities give insights into its low-energy properties. Similar to the prediction of the large N approximation, gapless spin and charge modes appear at the large Fermi wave vector. The highly suppressed spin velocity is a manifestation of "heavy" Luttinger liquid quasiparticles. A low-energy hybridization gap is detected at the small (conduction band) Fermi wave vector. In contrast to the exponential suppression of the Fermi velocity in the large-N approximation, we fit the spin velocity by a density-dependent power law of the Kondo coupling. The differences between the large-N theory and our numerical results are associated with the emergent magnetic Ruderman-Kittel-Kasuya-Yosida interactions.

Identifying a bath-induced bose liquid in interacting spin-boson models.

We study the ground state phase diagram of a one-dimensional hard-core bosonic model with nearest-neighbor interactions (XXZ model) where every site is coupled Ohmically to an independent but identical reservoir, hereby generalizing spin-boson models to interacting spin-boson systems. We show that a bath-induced Bose liquid phase can occur in the ground state phase diagram away from half filling. This phase is compressible, gapless, and conducting but not superfluid. At half filling, only a Luttinger liquid and a charge density wave are found. The phase transition between them is of Kosterlitz-Thouless type where the Luttinger parameter takes a nonuniversal value. The applied quantum Monte Carlo method can be used for all open bosonic and unfrustrated spin systems, regardless of their dimension, filling factor, and spectrum of the dissipation as long as the quantum system couples to the bath via the density operators.

Nature of the spin-liquid ground state of the S=1/2 Heisenberg model on the kagome lattice.

We perform a density-matrix renormalization group (DMRG) study of the S=1/2 Heisenberg antiferromagnet on the kagome lattice to identify the conjectured spin liquid ground state. Exploiting SU(2) spin symmetry, which allows us to keep up to 16,000 DMRG states, we consider cylinders with circumferences up to 17 lattice spacings and find a spin liquid ground state with an estimated per site energy of -0.4386(5), a spin gap of 0.13(1), very short-range decay in spin, dimer and chiral correlation functions, and finite topological entanglement γ consistent with γ=log(2)2, ruling out gapless, chiral, or nontopological spin liquids in favor of a topological spin liquid of quantum dimension 2, with strong evidence for a gapped topological Z(2) spin liquid.

The density-matrix renormalization group: a short introduction.

The density-matrix renormalization group (DMRG) method has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensional strongly correlated quantum lattice systems. The DMRG is a method that shares features of a renormalization group procedure (which here generates a flow in the space of reduced density operators) and of a variational method that operates on a highly interesting class of quantum states, so-called matrix product states (MPSs). The DMRG method is presented here entirely in the MPS language. While the DMRG generally fails in larger two-dimensional systems, the MPS picture suggests a straightforward generalization to higher dimensions in the framework of tensor network states. The resulting algorithms, however, suffer from difficulties absent in one dimension, apart from a much more unfavourable efficiency, such that their ultimate success remains far from clear at the moment.

Effect of electron-electron interactions on the charge carrier transitions in trans-polyacetylene.

By employing a newly developed nonadiabatic dynamical simulation method, which is a combination of classical molecular dynamics and the adaptive time-dependent density matrix renormalization group, we investigate the dynamics of charge carrier transitions in trans-polyacetylene (PA) with the inclusion of both electron-phonon and electron-electron interactions. The calculations are performed within a modified Su-Schrieffer-Heeger model in which electron-electron interactions are taken into account via the combination with extended Hubbard model (EHM). We find that removing an electron from a trans-PA chain bearing a positively charged polaron leads to the formation of a pair of charged solitons. Furthermore, we study the effect of electron-electron interactions on such charge carrier transitions in trans-PA. Our results show that increasing the on-site Coulomb interaction and the nearest-neighbor Coulomb repulsion will not change the qualitative behavior of the transition from a polaron to a soliton pair in the evolution process but will quantitatively reduce the moving velocities of the both formed solitons significantly and change the conditions for the soliton collisions.

Dynamical simulations of polaron transport in conjugated polymers with the inclusion of electron-electron interactions.

Dynamical simulations of polaron transport in conjugated polymers in the presence of an external time-dependent electric field have been performed within a combined extended Hubbard model (EHM) and Su-Schrieffer-Heeger (SSH) model. Nearly all relevant electron-phonon and electron-electron interactions are fully taken into account by solving the time-dependent Schrödinger equation for the pi electrons and the Newton's equation of motion for the backbone monomer displacements by virtue of the combination of the adaptive time-dependent density matrix renormalization group (TDDMRG) and classical molecular dynamics (MD). We find that after a smooth turn-on of the external electric field, the polaron is accelerated at first and then moves with a nearly constant velocity as one entity consisting of both the charge and the lattice deformation. An ohmic region (3 < or = E0 < or = 9 mV/A) where the stationary velocity increases linearly with the electric field strength is observed for the case of U = 2.0 eV and V = 1.0 eV. The maximal velocity is well above the speed of sound. Below 3 mV/A, the polaron velocity increases nonlinearly, and in high electric fields with strengths of E0 > or = 10.0 mV/A, the polaron will become unstable and dissociate. The relationship between electron-electron interaction strengths and polaron transport is also studied in detail. We find that the on-site Coulomb interactions U will suppress the polaron transport, and small nearest-neighbor interactions V values are also not beneficial to the polaronic motion while large V values favor the polaron transport.

Dynamical simulations of charged soliton transport in conjugated polymers with the inclusion of electron-electron interactions.

We present numerical studies of the transport dynamics of a charged soliton in conjugated polymers under the influence of an external time-dependent electric field. All relevant electron-phonon and electron-electron interactions are nearly fully taken into account by simulating the monomer displacements with classical molecular dynamics and evolving the wave function for the pi electrons by virtue of the adaptive time-dependent density matrix renormalization group simultaneously and nonadiabatically. It is found that after a smooth turn on of the external electric field the charged soliton is accelerated at first up to a stationary constant velocity as one entity consisting of both the charge and the lattice deformation. An Ohmic region (6 mV/A

d-Wave resonating valence bond states of fermionic atoms in optical lattices.

We study controlled generation and measurement of superfluid d-wave resonating valence bond (RVB) states of fermionic atoms in 2D optical lattices. Starting from loading spatial and spin patterns of atoms in optical superlattices as pure quantum states from a Fermi gas, we adiabatically transform this state to an RVB state by a change of the lattice parameters. Results of exact time-dependent numerical studies for ladders systems are presented, suggesting generation of RVB states on a time scale smaller than typical experimental decoherence times.

Real-time dynamics in spin-1/2 chains with adaptive time-dependent density matrix renormalization group.

We investigate the influence of different interaction strengths and dimerizations on the magnetization transport in antiferromagnetic spin 1/2 XXZ chains. We focus on the real-time evolution of the inhomogeneous initial state |upward arrow... upward arrow downward arrow... downward arrow > in using the adaptive time-dependent density-matrix renormalization group (adaptive t-DMRG). Time scales accessible to us are of the order of 100 units of time measured in Planck's/J for almost negligible error in the observables. We find ballistic magnetization transport for small S(z) S(z) interaction and arbitrary dimerization, but almost no transport for stronger S(z) S(z) interaction, with a sharp crossover at J(z) =1 . Additionally, we perform a detailed analysis of the error made by the adaptive time-dependent DMRG using the fact that the evolution in the XX model is known exactly. We find that the error at small times is dominated by the error made by the Trotter decomposition, whereas for longer times the DMRG truncation error becomes the most important, with a very sharp crossover at some "runaway" time. Overall, errors are extremely small before the "runaway" time.