Density Matrix Renormalization Group Research Articles

Multiversality and Unnecessary Criticality in One Dimension.

We present microscopic models of spin ladders which exhibit continuous critical surfaces whose properties and existence, unusually, cannot be inferred from those of the flanking phases. These models exhibit either "multiversality"-the presence of different universality classes over finite regions of a critical surface separating two distinct phases-or its close cousin, "unnecessary criticality"-the presence of a stable critical surface within a single, possibly trivial, phase. We elucidate these properties using Abelian bosonization and density-matrix renormalization-group simulations, and attempt to distill the key ingredients required to generalize these considerations.

Observation of a magnetic phase transition in monolayer NiPS3

Monolayer magnet of $\mathit{XY}$ type composes a pivotal part of the two-dimensional magnetism. As an important suspected $\mathit{XY}$-type antiferromagnet, whether $1L \mathrm{NiP}{\mathrm{S}}_{3}$ exhibits magnetic order remains elusive. Herein by helicity-resolved Raman and ultrafast spectroscopy of $\mathrm{NiP}{\mathrm{S}}_{3}$ from bulk to monolayer, we find that $1L \mathrm{NiP}{\mathrm{S}}_{3}$ is magnetically ordered with a Berezinskii-Kosterlitz-Thouless (BKT) transition at ${T}_{\mathrm{BKT}}\ensuremath{\approx}140$ K. We have also performed large-scale density-matrix renormalization-group calculations to verify the ground state zigzag antiferromagnetic order and Monte Carlo simulation to confirm the BKT-transition temperature in $1L \mathrm{NiP}{\mathrm{S}}_{3}$. Our investigations establish $1L \mathrm{NiP}{\mathrm{S}}_{3}$ to be an $\mathit{XY}$ antiferromagnet with a relatively high-temperature BKT transition, providing an important platform for investigating complex couplings and topological excitations.

Controlled Bond Expansion for Density Matrix Renormalization Group Ground State Search at Single-Site Costs

DMRG ground state search algorithms employing symmetries must be able to expand virtual bond spaces by adding or changing symmetry sectors if these lower the energy. Traditional single-site DMRG does not allow bond expansion; two-site DMRG does, but at much higher computational costs. We present a controlled bond expansion (CBE) algorithm that yields two-site accuracy and convergence per sweep, at single-site costs. Given a matrix product state $\mathrm{\ensuremath{\Psi}}$ defining a variational space, CBE identifies parts of the orthogonal space carrying significant weight in $H\mathrm{\ensuremath{\Psi}}$ and expands bonds to include only these. CBE-DMRG uses no mixing parameters and is fully variational. Using CBE-DMRG, we show that the Kondo-Heisenberg model on a width 4 cylinder features two distinct phases differing in their Fermi surface volumes.

Boundary quantum phase transitions in the spin- 12 Heisenberg chain with boundary magnetic fields

We consider the spin $\frac{1}{2}$ Heisenberg chain with boundary magnetic fields and analyze it using a combination of Bethe ansatz and density matrix renormalization group (DMRG) techniques. We show that the system exhibits several different ground states which depend on the orientation of the boundary magnetic fields. When both the boundary fields take equal values greater than a critical field strength, each edge in the ground state accumulates a fractional spin which saturates to spin $\frac{1}{4}$, which is similar to systems exhibiting symmetry protected topological phases (SPT). Unlike in SPT systems, the fractional boundary spin in the Heisenberg spin chain is not a genuine quantum number since the variance of the associated operator does not vanish, this is due to the absence of a bulk gap. The system exhibits high energy bound states when the boundary fields take values greater than the critical field. All the excitations in the system can be sorted out into towers whose number depends on the number of bound states exhibited by the system. As the boundary fields are varied, in addition to the ground state phase transition, we find that the system may undergo an eigenstate phase transition (EPT) where the number of towers of the Hilbert space changes. We further inquire how the EPT reflects itself on local ground state properties by computing the magnetization profile $\langle S^z_j \rangle$ using DMRG. We identify a clear qualitative change from low edge fields to high edge fields when crossing the critical field. We though are unable to conclude on the basis of our data that EPT corresponds to a genuine phase transition in the ground state.

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.

Pair density wave in the doped three-band Hubbard model on two-leg square cylinders

A pair density wave (PDW) is a superconducting (SC) state with a spatially modulated order parameter. Although much is known about the properties of the PDW state, its realization in microscopic models with divergent susceptibility has been challenging. Here we report a density-matrix renormalization group study of a three-band Hubbard model (also known as the Emery model) for cuprates on long two-leg square cylinders. Upon light doping, we find that the ground state of the system is consistent with that of a PDW state with mutually commensurate and power-law SC, charge (CDW), and spin (SDW) density wave correlations. The SC correlations are dominant between neighboring Cu sites with $d$-wave pairing symmetry. Interestingly, we find that the near-neighbor interactions, especially the near-neighbor attractive ${V}_{pd}$ interaction between neighboring Cu and oxygen sites, can notably enhance the SC correlations while simultaneously suppressing the CDW correlations. For a modestly strong attractive ${V}_{pd}$, the SC correlations become quasi-long-ranged with a divergent PDW susceptibility.

Superconductivity in doped triangular Mott insulators: The roles of parent spin backgrounds and charge kinetic energy

We study the prerequisites for realizing superconductivity in doped triangular-lattice Mott insulators by considering three distinct parent spin backgrounds, i.e., ${120}^{\ensuremath{\circ}}$ antiferromagnets, quantum spin liquid, and stripy antiferromagnets, and all possible sign combinations $({\ensuremath{\tau}}_{1},{\ensuremath{\tau}}_{2})$ of nearest-neighbor hopping and next-nearest-neighbor hopping $({t}_{1},{t}_{2})$. Based on density matrix renormalization group calculations, we find that, with finite ${t}_{2}$ and specific sign combinations $({\ensuremath{\tau}}_{1},{\ensuremath{\tau}}_{2})$, the quasi-long-range superconductivity order can always be achieved, regardless of the nature of the parent spin backgrounds. Besides specific hopping signs $({\ensuremath{\tau}}_{1},{\ensuremath{\tau}}_{2})$, these superconductivity phases in triangular lattices are commonly characterized by short-ranged spin correlations and two charges per stripe. In the robust superconductivity phase realized at larger ${t}_{2}/{t}_{1}$, flipping the signs ${\ensuremath{\tau}}_{2}$ and ${\ensuremath{\tau}}_{1}$ gives rise to the stripe phase without strong pairing and a pseudogaplike phase without Cooper-pair phase coherence, respectively. Interestingly, the roles of the two hopping signs are switched at smaller ${t}_{2}/{t}_{1}$. Moreover, different sign combinations $({\ensuremath{\tau}}_{1},{\ensuremath{\tau}}_{2})$ would stabilize distinct phases including superconductivity, charge density waves, spin density waves, and pseudogaplike phases accordingly. Our findings suggest the important role of charge kinetic energy in realizing superconductivity in doped triangular-lattice Mott insulators.

Ground-state and spectral properties of the doped one-dimensional optical Hubbard-Su-Schrieffer-Heeger model

We present a density matrix renormalization group study of the doped one-dimensional (1D) Hubbard-Su-Schrieffer-Heeger (Hubbard-SSH) model, where the atomic displacements linearly modulate the nearest-neighbor hopping integrals. Focusing on an optical variant of the model in the strongly correlated limit relevant for cuprate spin chains, we examine how the SSH interaction modifies the model's ground- and excited-state properties. The SSH coupling weakly renormalizes the model's single- and two-particle response functions for electron-phonon $(e\text{\ensuremath{-}}\mathrm{ph})$ coupling strengths below a parameter-dependent critical value ${g}_{\mathrm{c}}$. For larger $e\text{\ensuremath{-}}\mathrm{ph}$ coupling, the sign of the effective hopping integrals changes for a subset of orbitals, which drives a lattice dimerization distinct from the standard nesting-driven picture in 1D. The spectral weight of the one- and two-particle dynamical response functions are dramatically rearranged across this transition, with significant changes in the ground-state correlations. We argue that this dimerization results from the breakdown of the linear approximation for the $e\text{\ensuremath{-}}\mathrm{ph}$ coupling and thus signals a fundamental limitation of the linear SSH interaction. Our results have consequences for our understanding of how SSH-like interactions can enter the physics of strongly correlated quantum materials, including the recently synthesized doped cuprate spin chains.

Non-Abelian anyons with Rydberg atoms

We study the emergence of topological matter in two-dimensional systems of neutral Rydberg atoms in Ruby lattices. While Abelian anyons have been predicted in such systems, non-Abelian anyons, which would form a substrate for fault-tolerant quantum computing, have not been generated. To generate anyons with non-Abelian braiding statistics, we consider systems with mixed-boundary punctures. We obtain the topologically distinct ground states of the system numerically using the infinite Density Matrix Renormalization Group technique. We discuss how these topological states can be created using ancilla atoms of a different type. We show that a system with $2N+2$ punctures and an equal number of ancilla atoms leads to $N$ logical qubits whose Hilbert space is determined by a set of stabilizing conditions on the ancilla atoms. Quantum gates can be implemented using a set of gates acting on the ancilla atoms that commute with the stabilizers and realize the braiding group of non-Abelian Ising anyons.

Triangular lattice Hubbard model physics at intermediate temperatures

Moire systems offer an exciting playground to study many-body effects of strongly correlated electrons in regimes that are not easily accessible in conventional material settings. Motivated by a recent experiment on $\text{WSe}_2/\text{WS}_2$ moire bilayers [Y. Tang et al., Nature 579, 353-358 (2020)], which realizes a triangular superlattice with a small hopping (of approximately 10 Kelvin), with tunable density of holes, we explore the Hubbard model on the triangular lattice for intermediate temperatures $t \lesssim T < U$. Employing finite temperature Lanczos calculations, and closely following the fitting protocols used in the experiment, we recover the observed trends in the reported Curie-Weiss temperature $\Theta$ with filling, using the reported interaction strength $U/t=20$. We focus on the large increase of $|\Theta|$ on decreasing the density below half filling and the sign change of $\Theta$ at higher fillings, which signals the onset of ferromagnetism. The increase in $|\Theta|$ is also seen in the $t$-$J$ model (the low energy limit of the Hubbard model) in the intermediate temperature range, which we clarify is opposite to the trend in its high temperature limit. Differences between the low, intermediate and high temperature regimes are discussed. Our numerical calculations also capture the crossover between short-range antiferromagnetic to ferromagnetic order in the intermediate temperature regime, a result broadly consistent with the experimental findings. We find that this behavior is a finite-temperature remnant of the underlying zero temperature phase transition, which we explore with ground state density matrix renormalization group calculations. We provide evidence of ferromagnetism characterized by weak (but robust) correlations that explain the small $\Theta$ seen in the experiment.

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.

Plaquette valence bond state in the spin- 12 J1−J2 XY model on the square lattice

We studied the ground-state phase diagram of spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2} XY$ model on the square lattice with first-neighbor ${J}_{1}$ and second-neighbor ${J}_{2}$ antiferromagnetic interactions using both infinite density matrix renormalization group (iDMRG) and DMRG approaches. We show that a plaquette valence bond phase is realized in an intermediate region $0.50\ensuremath{\le}{J}_{2}/{J}_{1}&lt;0.54$ between a N\'eel magnetic ordered phase at ${J}_{2}/{J}_{1}&lt;0.50$ and a stripy magnetic ordered phase at ${J}_{2}/{J}_{1}\ensuremath{\ge}0.54$. The plaquette valence bond phase is characterized by finite dimer orders in both the horizontal and vertical directions. Contrary to the spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model, we do not find numerical evidence for a quantum spin liquid phase in the ${J}_{1}\text{\ensuremath{-}}{J}_{2} XY$ model.

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).

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.

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.

Hierarchical Clifford Transformations to Reduce Entanglement in Quantum Chemistry Wave Functions.

The performance of computational methods for many-body physics and chemistry is strongly dependent on the choice of the basis used to formulate the problem. Hence, the search for similarity transformations that yield better bases is important for progress in the field. So far, tools from theoretical quantum information have not been thoroughly explored for this task. Here we take a step in this direction by presenting efficiently computable Clifford similarity transformations for the molecular electronic structure Hamiltonian, which expose bases with reduced entanglement in the corresponding molecular ground states. These transformations are constructed via block-diagonalization of a hierarchy of truncated molecular Hamiltonians, preserving the full spectrum of the original problem. We show that the bases introduced here allow for more efficient classical and quantum computations of ground-state properties. First, we find a systematic reduction of bipartite entanglement in molecular ground states as compared to standard problem representations. This entanglement reduction has implications in classical numerical methods, such as those based on the density matrix renormalization group. Then, we develop variational quantum algorithms that exploit the structure in the new bases, showing again improved results when the hierarchical Clifford transformations are used.

Quench dynamics in the one-dimensional mass-imbalanced ionic Hubbard model

Using the time-dependent Lanczos method, we study the nonequilibrium dynamics of the one-dimensional ionic-mass imbalanced Hubbard chain driven by a quantum quench of the on-site Coulomb interaction, where the system is prepared in the ground state of the Hamiltonian with a different Hubbard interaction. The exact diagonalization method (Lanczos algorithm) is adopted to study the zero temperature phase diagram in equilibrium, which is shown to be in good agreement with previous studies using density matrix renormalization group (DMRG). We then study the nonequilibrium quench dynamics of the spin and charge order parameters by fixing the initial and final Coulomb interactions while changing the quenching time protocols. Our study shows that the time evolution of the charge and spin order parameters strongly depend on the quenching time protocols. In particular, the effective temperature of the system will decrease monotonically as the quenching time is increased. By taking the final Coulomb interaction strength to be in the strong coupling regime, we find that the oscillation frequency of the charge order parameter increases monotonically with the Coulomb interaction. By contrast, the frequency of the spin order parameter decreases monotonically with increasing Coulomb interaction. We explain this result using an effective spin model and a two-site Hubbard model in the strong coupling limit. Finally, we take the final Coulomb interaction strength to be in the weak coupling regime and find that the oscillation frequency of both the charge and spin order parameters increases monotonically with decreasing Coulomb interaction. Our study suggests strategies to engineer the relaxation behavior of interacting quantum many-particle systems.

Quantum criticality of a Z_{3}-symmetric spin chain with long-range interactions.

Based on large-scale density matrix renormalization group techniques, we investigate the critical behaviors of quantum three-state Potts chains with long-range interactions. Using fidelity susceptibility as an indicator, we obtain a complete phase diagram of the system. The results show that as the long-range interaction power α increases, the critical points f_{c}^{*} shift towards lower values. In addition, the critical threshold α_{c}(≈1.43) of the long-range interaction power is obtained for the first time by a nonperturbative numerical method. This indicates that the critical behavior of the system can be naturally divided into two distinct universality classes, namely the long-range (α<α_{c}) and short-range (α>α_{c}) universality classes, qualitatively consistent with the classical ϕ^{3} effective field theory. This work provides a useful reference for further research on phase transitions in quantum spin chains with long-range interaction.

Enhanced superconductivity by near-neighbor attraction in the doped extended Hubbard model

Recent experiment has unveiled an anomalously strong electron-electron attraction in one-dimensional copper-oxide chain Ba$_{2-x}$Sr$_x$CuO$_{3+\delta}$. While the near-neighbor electron attraction $V$ in the one-dimensional extended Hubbard chain has been examined recently, its effect in the Hubbard model beyond the one-dimensional chain remains unclear. We report a density-matrix renormalization group study of the extended Hubbard model on long four-leg cylinders on the square lattice. We find that the near-neighbor electron attraction $V$ can notably enhance the long-distance superconducting correlations while simultaneously suppressing the charge-density-wave correlations. Specifically, for a modestly strong electron attraction, the superconducting correlations become dominant over the CDW correlations with a Luttinger exponent $K_{sc}\sim 1$ and strong divergent superconducting susceptibility. Our results provide a promising way to realize long-range superconductivity in the doped Hubbard model in two dimensions. The relevance of our numerical results to cuprate materials is also discussed.

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.