Density Matrix Renormalization Group Method Research Articles

Quantum Criticality and Universal Behavior in Molecular Dipolar Lattices of Endofullerenes

Fullerene cages allow the confinement of single molecules and the construction of molecular assemblies whose properties strongly differ from those of free species. In this work, we employ the density-matrix renormalization group method to show that chains of fullerenes filled with polar molecules (LiF, HF, and H2O) can form dipole-ordered quantum phases. In symmetry broken environments, these ordered phases are ferroelectric, a property that makes them promising candidates for quantum devices. We demonstrate that for a given guest molecule, the occurrence of these quantum phases can be enforced or influenced either by changing the effective electric dipole moment or by isotopic substitution. In the ordered phase, all systems under consideration are characterized by universal behavior that depends only on the ratio of the effective electric dipole and of the rotational constant. A phase diagram is derived, and further molecules are proposed as candidates for dipole-ordered endofullerene chains.

High-Performance Computing for Density Matrix Renormalization Group

Abstract: In the last decades, many algorithms have been developed to use high-performance computing (HPC) techniques to accelerate the density matrix renormalization group (DMRG) method, an effective method for solving large active space strong correlation problems. In this article, the previous DMRG parallelization algorithms at different levels of the parallelism are introduced. The heterogeneous computing acceleration methods and the mixed-precision implementation are also presented and discussed. This mini-review concludes with some summary and prospects for future works.

Traces of electron-phonon coupling in one-dimensional cuprates

The appearance of certain spectral features in one-dimensional (1D) cuprate materials has been attributed to a strong, extended attractive coupling between electrons. Here, using time-dependent density matrix renormalization group methods on a Hubbard-extended Holstein model, we show that extended electron-phonon (e–ph) coupling presents an obvious choice to produce such an attractive interaction that reproduces the observed spectral features and doping dependence seen in angle-resolved photoemission experiments: diminished 3kF spectral weight, prominent spectral intensity of a holon-folding branch, and the correct holon band width. While extended e–ph coupling does not qualitatively alter the ground state of the 1D system compared to the Hubbard model, it quantitatively enhances the long-range superconducting correlations and suppresses spin correlations. Such an extended e–ph interaction may be an important missing ingredient in describing the physics of the structurally similar two-dimensional high-temperature superconducting layered cuprates, which may tip the balance between intertwined orders in favor of uniform d-wave superconductivity.

Bose-Einstein condensation in honeycomb dimer magnets and Yb2Si2O7

An asymmetric Bose-Einstein condensation (BEC) dome was observed in a recent experiment on the quantum dimer magnet ${\mathrm{Yb}}_{2}{\mathrm{Si}}_{2}{\mathrm{O}}_{7}\mathrm{e}$ [G. Hester et al., Phys. Rev. Lett. 123, 027201 (2019)], which is modeled by a ``breathing'' honeycomb lattice Heisenberg model with possible anisotropies. We report a remarkable agreement between key experimental features and predictions from numerical simulations of the magnetic model. Both critical fields, as well as critical temperatures of the BEC dome, can be accurately captured, as well as the occurrence of two regimes inside the BEC phase. Furthermore, we investigate the role of anisotropies in the exchange coupling and the $g$ tensor. While we confirm a previous proposal that anisotropy can induce a zero-temperature phase transition at magnetic fields smaller than the fully polarizing field strength, we find that this effect becomes negligible at temperatures above the anisotropy scale. Instead, the two regimes inside the BEC dome are found to be due to a nonlinear magnetization behavior of the isotropic breathing honeycomb Heisenberg antiferromagnet. Our analysis is performed by combining the density matrix renormalization group (DMRG) method with the finite-temperature techniques of minimally entangled typical thermal states (METTS) and quantum Monte Carlo (QMC).

DMRG analysis of magnetic order in the zigzag edges of hexagonal CrN nanoribbons

We investigate the finite-temperature magnetic order at the edges of hexagonal CrN nanoribbons by using density functional theory combined with the density matrix renormalization group (DMRG) method. Moreover, the spin-dependent transport in nanoribbons is calculated within the semiclassical Boltzmann transport theory. We find that the zigzag edges have lower energy with respect to armchair edges. The zigzag edges of CrN nanoribbon show half-metallic electronic character, which is the same as for the two-dimensional (2D) monolayer. The localized electronic states on the zigzag edges reduce the electronic band gap energy for spin-down electrons. The ab initio electronic results are mapped into an effective 1D Heisenberg spin model up to the next-nearest-neighbor exchange interaction term. For zigzag ribbons, the nearest-neighbor and next-nearest-neighbor magnetic exchange are around 10--12 and $\ensuremath{-}2$ to 0 $\text{meV}/\text{Cr}\phantom{\rule{4.pt}{0ex}}\text{atom}$, respectively. The finite spin correlation length in 1D nanoribbons drops sharply to zero with temperature. The absence of long-range spin correlations at the edges is a practical drawback for future room temperature 2D spintronic devices. The maximally localized Wannier functions are used for band interpolation and spin-dependent transport calculations by using the semiclassical Boltzmann equation. We show that the zigzag edges of CrN are a perfect spin filter under both electron and hole doping.

Dimensional crossover on multileg attractive- U Hubbard ladders

We study the ground state properties of a polarized two-component Fermi gas on multileg attractive-$U$ Hubbard ladders. Using exact diagonalization and density matrix renormalization group method simulations, we construct grand canonical phase diagrams for ladder widths of up to $W=5$ and varying perpendicular geometries, characterizing the quasi-one-dimensional regime of the dimensional crossover. We unveil a multicritical point marking the onset of partial polarization in those phase diagrams, a candidate regime of finite-momentum pairing. We compare our findings with recent experimental and theoretical studies of quasi-one-dimensional polarized Fermi gases.

Relation between the noise correlations and the spin structure factor for Mott-insulating states in SU(N) Hubbard models

It is well established that the noise correlations measured by time-of-flight imaging in cold-atom experiments, which correspond to the density-density correlations in the momentum space of trapped atomic gases, can probe the spin structure factor deep in the Mott-insulating regime of SU(2) Hubbard models. We explicitly derive the mathematical relation between the noise correlations and the spin structure factor in the strong-interaction limit of SU$(N)$ Hubbard models at any integer filling $\rho$. By calculating the ground states of one-dimensional SU$(N)$ Fermi-Hubbard models for $2\leq N\leq 6$ with use of the density-matrix renormalization-group method, we confirm the relation numerically in the regime of strong interactions $U \gg t$, where $U$ and $t$ denote the onsite interaction and the hopping energy. We show that the deviation between the actual noise correlations and those obtained from the spin structure factor scales as approximately $(t/U)^2$ for $\rho=1$ at intermediate and large lattice sizes on the basis of numeric and semi-analytic arguments.

Realization of a supersolid phase in a two-channel model

We construct a two-channel model based on the one-dimensional extended Bose–Hubbard model, by including a second channel of free bosons. We use the mean-field theory to map the system to a reduced single-channel one and solve this system by means of the density matrix renormalization group method. We find the region where the superfluid and density-wave orders coexist which signals a supersolid state. Our theory can be realized experimentally with state-dependent optical lattices.

On the stability of charge and spin order in the spin-one-half Falicov–Kimball model with the Ising-type Hund coupling

Density matrix renormalization group (DMRG) method is used to study effects of various factors on the stability of charge and spin order in the spin-one-half Falicov–Kimball model with the Ising-type Hund coupling Jz. In particular we examine effects of (i) the exchange interaction (J) between d and f electrons, which is responsible for spin-flip processes, (ii) the f-electron hopping (tf) and (iii) the interband d–f hybridization V. It is shown that for all mentioned generalizations there exists some critical value of the exchange interaction (Jc), the f-electron hopping (tfc) and the interband d–f hybridization Vc at which the magnetic order detected within the spin-one-half Falicov–Kimball model with the Ising interaction is broken. Above these critical points new types of spin orderings are generated, and namely, spin density waves commensurate with charge density waves detected at J=0 in the case of exchange interaction and spin separated phases in the case of f-electron hopping (hybridization), which are at sufficiently large tf (V) replaced by homogeneous phases.

First-order topological phase transitions and disorder-induced Majorana modes in interacting fermion chains

Using a combination of the mean-field Bogoliubov--de Gennes approach and the density matrix renormalization group method, we discover first-order topological transitions between topological superconducting and trivial insulating phases in a sawtooth lattice of intersite attractive fermions. The topological characterization of different phases is achieved in terms of winding numbers, Majorana edge modes, and entanglement spectra. By studying the effect of disorder on first-order topological phase transitions, we establish disorder-induced topological phase coexistence as a mechanism for generating a finite density of Majorana particles.

Schwinger model on an interval: Analytic results and DMRG

Quantum electrodynamics in $1+1$ dimensions (Schwinger model) on an interval admits lattice discretization with a finite-dimensional Hilbert space, and is often used as a testbed for quantum and tensor network simulations. In this work we clarify the precise mapping between the boundary conditions in the continuum and lattice theories. In particular we show that the conventional Gauss law constraint commonly used in simulations induces a strong boundary effect on the charge density, reflecting the appearance of fractionalized charges. Further, we obtain by bosonization a number of exact analytic results for local observables in the massless Schwinger model. We compare these analytic results with the simulation results obtained by the density matrix renormalization group (DMRG) method and find excellent agreements.

Where is the Quantum Spin Nematic?

We provide strong evidence of the spin-nematic state in a paradigmatic ferro-antiferromagnetic J_{1}-J_{2} model using analytical and density-matrix renormalization group methods. In zero field, the attraction of spin-flip pairs leads to a first-order transition and no nematic state, while pair repulsion at larger J_{2} stabilizes the nematic phase in a narrow region near the pair-condensation field. A devil's staircase of multipair condensates is conjectured for weak pair attraction. A suppression of the spin-flip gap by many-body effects leads to an order-of-magnitude contraction of the nematic phase compared to naïve expectations. The proposed phase diagram should be broadly valid.

Accessing the topological Mott insulator in cold atom quantum simulators with realistic Rydberg dressing

The interplay between many-body interactions and the kinetic energy gives rise to rich phase diagrams hosting, among others, interaction-induced topological phases. These phases are characterized by both a local order parameter and a global topological invariant, and can exhibit exotic ground states such as self-trapped polarons and interaction-induced edge states. In this work, we investigate a realistic scenario for the quantum simulation of such systems using cold Rydberg-dressed atoms in optical lattices. We consider spinless fermions on a checkerboard lattice, interacting via the tunable-range effective potential induced by the Rydberg dressing. We perform a detailed analysis of the phase diagram at half- and incommensurate fillings, in the mean-field approximation. We furthermore study the stability of the phases with respect to temperature within the mean-field approximation and with respect to quantum fluctuations using the density matrix renormalization group method. Finally, we propose an implementation protocol, and in particular identify attainable regimes of experimental parameters in which the topological properties of the model become accessible. Our work thereby opens a realistic pathway to the outstanding experimental observation of this predicted phase in state-of-the-art cold atom quantum simulators.

Pair binding and enhancement of pairing correlations in asymmetric Hubbard ladders

Asymmetric two-leg Hubbard ladders with different on-site interactions $U_y$ and hoppings $t_y$ on each leg are investigated using the density matrix renormalization group method and exact diagonalizations. The pairing found in symmetric ladders is robust against the introduction of the leg asymmetry. When studying pairing, one-band Hubbard ladder models are better described as one-dimensional correlated two-band models than as sublattices of higher dimensional systems. The asymmetric Hubbard ladder provides us with a simple model for studying pairing in the crossover regime between charge transfer and Mott insulators.

Topological quantum phase transition in a mixed-spin Heisenberg tetramer chain with alternating spin-1/2 and spin-5/2 dimers

We investigate magnetic quantum phases and the topological quantum phase transition between two distinct valence-bond solid (VBS) phases of a minimal interacting spin-chain model that captures a magnetic behavior of the novel low-dimensional quantum ferrimagnetic material Cu2Fe2Ge4O13. The studied mixed-spin Heisenberg tetramer chain consists of a 4-period array of spins involving two types of dimers sa−sa (sa=1/2) and Sb−Sb (Sb=5/2) under the assumption of unique intra- and inter-dimer coupling constants J1 and J2, respectively. Using the tensor-network formulation of the density-matrix renormalization group method, we have constructed the ground-state phase diagram in the parameter space magnetic field versus the interaction ratio J=J2/J1, whereby all ground states are in accordance with the Oshikawa–Yamanaka–Affleck theorem for a given period. In addition, we have implemented the recent tangential finite-size scaling method in order to characterize the critical behavior of the topological VBS transition through calculation of the critical point Jc and the critical exponent of the correlation length ν. Our results are consistent with the topological quantum phase transition from the SU(2) Wess–Zumino–Witten universality class with the critical exponent of correlation length ν=2/3 by assuming the proper logarithmic correction.

Exploring interacting topological insulator in the extended Su-Schrieffer-Heeger model

Exploring topological phases in interacting systems is a challenging task. We investigate many-body topological physics of interacting fermions in an extended Su-Schrieffer-Heeger (SSH) model, which extends the two sublattices of SSH model into four sublattices and thus is dubbed SSH4 model, based on the density-matrix renormalization-group numerical method. The interaction-driven phase transition from topological insulator to charge density wave (CDW) phase can be identified by analyzing the variations of entanglement spectrum, entanglement entropies, energy gaps, CDW order parameter, and fidelity. We map the global phase diagram of the many-body ground state, which contains nontrivial topological insulator, trivial insulator and CDW phases, respectively. In contrast to interacting SSH model, in which the phase transitions to the CDW phase are argued to be first-order phase transitions, the phase transitions between the CDW phase and topologically trivial/nontrivial phases are shown to be continuous phase transitions. Finally, we {also} show the phase diagram of interacting spinful SSH4 model, where the attractive (repulsive) on-site spin interaction amplifies (suppresses) the CDW phase. The models analyzed here can be implemented with ultracold atoms on optical superlattices.

Enhanced Intertwined Spin and Charge Orders in the t–J Model in a Small J Case

The one-band t–J model captures strong correlations in cuprate high-temperature superconductors. It accounts for the various intertwined spin and charge orders, and the superconductivity in the phase diagrams. To see the correlation effect on the intertwined orders, we implement the density matrix renormalization group method to simulate the t–J model in a small J case with t/J = 10, which is in a deeper Mott region than that with t/J ≃ 3 in cuprate superconducting compounds. We examine the results on a six-leg lattice with both the nearest and next-nearest-neighbor hoppings and antiferromagnetic coupling, and find the absence of superconductivity and enhanced intertwined spin and charge orders in the phase diagram. Besides the stripe phases, we find a new SDW + CDW phase in which the spin modulation is a (π, π) antiferromagnetism, while the wavelength of the charge modulation is shorter than that of the stripe phases. Our results suggest the enhanced intertwined orders and suppressed superconductivity in the deep Mott region.

Infinite density matrix renormalization group method for solving the Ising model

Infinite density matrix renormalization group method for solving the Ising model

Study of Interacting Heisenberg Antiferromagnet Spin-1/2 and 1 Chains

Haldane conjectures the fundamental difference in the energy spectrum of the Heisenberg antiferromagnetic (HAF) of the spin S chain is that the half-integer and the integer S chain have gapless and gapped energy spectrums, respectively. The ground state (gs) of the HAF spin-1/2 and spin-1 chains have a quasi-long-range and short-range correlation, respectively. We study the effect of the exchange interaction between an HAF spin-1/2 and an HAF spin-1 chain forming a normal ladder system and its gs properties. The inter-chain exchange interaction J⊥ can be either ferromagnetic (FM) or antiferromagnetic (AFM). Using the density matrix renormalization group method, we show that in the weak AFM/FM coupling limit of J⊥, the system behaves like two decoupled chains. However, in the large AFM J⊥ limit, the whole system can be visualized as weakly coupled spin-1/2 and spin-1 pairs which behave like an effective spin-1/2 HAF chain. In the large FM J⊥ limit, coupled spin-1/2 and spin-1 pairs can form pseudo spin-3/2 and the whole system behaves like an effective spin-3/2 HAF chain. We also derive the effective model Hamiltonian in both strong FM and AFM rung exchange coupling limits.

Projection-Based Density Matrix Renormalization Group in Density Functional Theory Embedding.

The density matrix renormalization group (DMRG) method has already proved itself as a very efficient and accurate computational method, which can treat large active spaces and capture the major part of strong correlation. Its application on larger molecules is, however, limited by its own computational scaling as well as demands of methods for treatment of the missing dynamical electron correlation. In this work, we present the first step in the direction of combining DMRG with density functional theory (DFT), one of the most employed quantum chemical methods with favorable scaling, by means of the projection-based wave function (WF)-in-DFT embedding. On two proof-of-concept but important molecular examples, we demonstrate that the developed DMRG-in-DFT approach provides a very accurate description of molecules with a strongly correlated fragment.