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Register a new userPeriodically Driven Many-Body Systems: A Floquet Density Matrix Renormalization Group Study
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Driving a quantum system periodically in time can profoundly alter its long-time correlations and give rise to exotic quantum states of matter. The complexity of the combination of many-body correlations and dynamic manipulations has the potential to uncover a whole field of new phenomena, but the theoretical and numerical understanding becomes extremely difficult. We now propose a promising numerical method by generalizing the density matrix renormalization group to a superposition of Fourier components of periodically driven many-body systems using Floquet theory. With this method we can study the full time-dependent quantum solution in a large parameter range for all evolution times, beyond the commonly used high-frequency approximations. Numerical results are presented for the isotropic Heisenberg antiferromagnetic spin-1/2 chain under both local(edge) and global driving for spin-spin correlations and temporal fluctuations. As the frequency is lowered, we demonstrate that more and more Fourier components become relevant and determine strong length- and frequency-dependent changes of the quantum correlations that cannot be described by effective static models.
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In some cases the state of a quantum system with a large number of subsystems can be approximated efficiently by the density matrix renormalization group, which makes use of redundancies in the description of the state. Here we show that the achievable efficiency can be much better when performing density matrix renormalization group calculations in the Heisenberg picture, as only the observable of interest but not the entire state is considered. In some non-trivial cases, this approach can even be exact for finite bond dimensions.
We establish some general dynamical properties of lattice many-body systems that are subject to a high-frequency periodic driving. We prove that such systems have a quasi-conserved extensive quantity $H_*$, which plays the role of an effective static Hamiltonian. The dynamics of the system (e.g., evolution of any local observable) is well-approximated by the evolution with the Hamiltonian $H_*$ up to time $tau_*$, which is exponentially long in the driving frequency. We further show that the energy absorption rate is exponentially small in the driving frequency. In cases where $H_*$ is ergodic, the driven system prethermalizes to a thermal state described by $H_*$ at intermediate times $tlesssim tau_*$, eventually heating up to an infinite-temperature state at times $tsim tau_*$. Our results indicate that rapidly driven many-body systems generically exhibit prethermalization and very slow heating. We briefly discuss implications for experiments which realize topological states by periodic driving.
We introduce the transcorrelated Density Matrix Renormalization Group (tcDMRG) theory for the efficient approximation of the energy for strongly correlated systems. tcDMRG encodes the wave function as a product of a fixed Jastrow or Gutzwiller correlator and a matrix product state. The latter is optimized by applying the imaginary-time variant of time-dependent (TD) DMRG to the non-Hermitian transcorrelated Hamiltonian. We demonstrate the efficiency of tcDMRG at the example of the two-dimensional Fermi-Hubbard Hamiltonian, a notoriously difficult target for the DMRG algorithm, for different sizes, occupation numbers, and interaction strengths. We demonstrate fast energy convergence of tcDMRG, which indicates that tcDMRG could increase the efficiency of standard DMRG beyond quasi-monodimensional systems and provides a generally powerful approach toward the dynamic correlation problem of DMRG.
A quantum dot coupled to ferromagnetically polarized one-dimensional leads is studied numerically using the density matrix renormalization group method. Several real space properties and the local density of states at the dot are computed. It is shown that this local density of states is suppressed by the parallel polarization of the leads. In this case we are able to estimate the length of the Kondo cloud, and to relate its behavior to that suppression. Another important result of our study is that the tunnel magnetoresistance as a function of the quantum dot on-site energy is minimum and negative at the symmetric point.
We show how lattice gauge theories can display many-body localization dynamics in the absence of disorder. Our starting point is the observation that, for some generic translationally invariant states, Gauss law effectively induces a dynamics which can be described as a disorder average over gauge super-selection sectors. We carry out extensive exact simulations on the real-time dynamics of a lattice Schwinger model, describing the coupling between U(1) gauge fields and staggered fermions. Our results show how memory effects and slow entanglement growth are present in a broad regime of parameters - in particular, for sufficiently large interactions. These findings are immediately relevant to cold atoms and trapped ions experiments realizing dynamical gauge fields, and suggest a new and universal link between confinement and entanglement dynamics in the many-body localized phase of lattice models.
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