Density Matrix Renormalization Group Study Research Articles

Quantum criticality in chains of planar rotors with dipolar interactions.

In this work, we perform a density matrix renormalization group study of chains of planar rotors interacting via dipolar interactions. By exploring the ground state from weakly to strongly interacting rotors, we find the occurrence of a quantum phase transition between a disordered and a dipole-ordered quantum state. We show that the nature of the ordered state changes from ferroelectric to antiferroelectric when the relative orientation of the rotor planes varies and that this change requires no modification of the overall symmetry. The observed quantum phase transitions are characterized by critical exponents and central charges, which reveal different universality classes ranging from that of the (1 + 1)D Ising model to the 2D classical XY model.

Pair density wave and superconductivity in a kinetically frustrated doped Emery model on a square lattice

The quest to understand the nature of superconductivity in the cuprates has spotlighted the pair density wave (PDW)–a superconducting state characterized by a spatially modulated order parameter. Despite significant advances in understanding PDW properties, conclusively demonstrating its presence in systems pertinent to cuprate superconductors remains elusive. In this study, we present a systematic density-matrix renormalization group study to investigate the Emery model (or the three-band Hubbard model) on two-leg square cylinders with negative electron hopping term tpp between adjacent oxygen sites. Kinetic frustration - introduced by changing the sign of oxygen-oxygen hopping - leads to a much reduced Cu-Cu antiferromagnetic exchange along with an enlarged charge transfer energy that changes the local properties of the model. At light doping levels, our findings reveal a ground state remarkably consistent with a PDW, exhibiting mutually commensurate superconducting (SC), charge, and spin density wave correlations. Intriguingly, the dominant SC pairing is observed between neighboring oxygen sites, diverging from the expected Cu sites in the positive tpp case. When the system incorporates moderate near-neighbor interactions, particularly an attractive Vpp between adjacent oxygen sites, the SC correlations become quasi-long-ranged, accompanied by a pronounced divergence in the PDW susceptibility. When the attractive Vpp increases further, the system gives way to an unconventional d-wave superconductivity.

Effective Bi-Layer Model Hamiltonian and Density-Matrix Renormalization Group Study for the High-T c Superconductivity in La3Ni2O7 under High Pressure

High-T c superconductivity with possible T c ≈ 80 K has been reported in the single crystal of La3Ni2O7 under high pressure. Based on the electronic structure given by the density functional theory calculations, we propose an effective bi-layer model Hamiltonian including both 3d z 2 and 3d x 2–y 2 orbital electrons of the nickel cations. The main feature of the model is that the 3d z 2 electrons form inter-layer σ-bonding and anti-bonding bands via the apical oxygen anions between the two layers, while the 3d x 2–y 2 electrons hybridize with the 3d z 2 electrons within each NiO2 plane. The chemical potential difference of these two orbital electrons ensures that the 3d z 2 orbitals are close to half-filling and the 3d x 2–y 2 orbitals are near quarter-filling. The strong on-site Hubbard repulsion of the 3d z 2 orbital electrons gives rise to an effective inter-layer antiferromagnetic spin super-exchange J. Applying pressure can self dope holes on the 3d z 2 orbitals with the same amount of electrons doped on the 3d x 2–y 2 orbitals. By performing numerical density-matrix renormalization group calculations on a minimum setup and focusing on the limit of large J and small doping of 3d z 2 orbitals, we find the superconducting instability on both the 3d z 2 and 3d x 2–y 2 orbitals by calculating the equal-time spin singlet pair–pair correlation function. Our numerical results may provide useful insights in the high-T c superconductivity in single crystal La3Ni2O7 under high pressure.

Emergent glassiness in the disorder-free Kitaev model: Density matrix renormalization group study on a one-dimensional ladder setting

Emergent glassiness in the disorder-free Kitaev model: Density matrix renormalization group study on a one-dimensional ladder setting

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.

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.

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.

Quantum Phase Diagram and Spontaneously Emergent Topological Chiral Superconductivity in Doped Triangular-Lattice Mott Insulators.

The topological superconducting state is a highly sought-after quantum state hosting topological order and Majorana excitations. In this Letter, we explore the mechanism to realize the topological superconductivity (TSC) in the doped Mott insulators with time-reversal symmetry (TRS). Through large-scale density matrix renormalization group study of an extended triangular-lattice t-J model on the six- and eight-leg cylinders, we identify a d+id-wave chiral TSC with spontaneous TRS breaking, which is characterized by a Chern number C=2 and quasi-long-range superconducting order. We map out the quantum phase diagram with by tuning the next-nearest-neighbor (NNN) electron hopping and spin interaction. In the weaker NNN-coupling regime, we identify a pseudogaplike phase with a charge stripe order coexisting with fluctuating superconductivity, which can be tuned into d-wave superconductivity by increasing the doping level and system width. The TSC emerges in the intermediate-coupling regime, which has a transition to a d-wave superconducting phase with larger NNN couplings. The emergence of the TSC is driven by geometrical frustrations and hole dynamics which suppress spin correlation and charge order, leading to a topological quantum phase transition.

Ground-state phase diagram of the extended two-leg t−J ladder

Inspired by the observation of a robust $d$-wave superconducting phase driven by tuning the next-nearest-neighbor (NNN) electron hopping in recent density matrix renormalization group (DMRG) studies of six- and eight-leg $t$-$J$ model, we systematically study the phase diagram of the two-leg $t$-$J$ ladder with the NNN couplings (including NNN hopping and spin interaction) in a large region of doping level, by means of the DMRG calculations. Upon doping from half filling, we identify the Luther-Emery liquid (LEL) phase, which can be distinguished as the pairing-dominant and charge density-dominant regime by comparing the Luttinger parameter $K_{\rho}$. With the growing NNN couplings, pairing correlations are enhanced and correspondingly $K_{\rho}$ increases, driving the system from the density-dominant to the pairing-dominant regime. In the Tomonaga-Luttinger liquid (TLL) phase in the larger doping region, we identify two TLL regimes with different features of charge density correlation. At the quarter filling ($1/2$ doping level), we find that the strong dimer orders of bond energy in the open system actually decay algebraically and thus do not indicate a spontaneous translational symmetry breaking. Our results show that in the LEL phase of the two-leg ladder, the NNN couplings seem to play the similar role as that on the wider $t$-$J$ cylinder, and studies on this more accessible system can be helpful towards understanding the emergence of the remarkable $d$-wave superconducting phase on the wider system.

From edge to bulk: Cavity-induced displacement of topological nonlocal qubits

We investigate the ability of selective cavity coupling to a topological chain for tailoring the connectivity of Majorana fermions. We show how topological qubits (TQs), associated with nonlocal Majorana fermion pairing, can be displaced from the edges to the bulk of a topological chain through selective access to light-matter interaction with specific physical sites. In particular, we present a comprehensive density matrix renormalization group study of ground-state features in different chain-cavity coupling geometries, and we validate analytical insights in the strong-coupling regime. This type of Majorana fermion correlation generation process comes with emergent cavity photon features. Moreover, by considering the time evolution after a sudden quench of the cavity-matter coupling strength, we show that the development of high nontrivial matter (Majorana) correlations leaves behind measurable nonclassical photon imprints in the cavity. Innovative ways to dynamically generate TQ nonlocal correlations in topological chains of arbitrary length are thus provided, opening alternative routes to controllable long-range entanglement in hybrid photonic solid-state systems.

Correlated Electronic States of Polycyclic Aromatic Hydrocarbons in Singlet Fission: A Density Matrix Renormalization Group Study

Correlated Electronic States of Polycyclic Aromatic Hydrocarbons in Singlet Fission: A Density Matrix Renormalization Group Study

DMRG study of the higher-charge Schwinger model and its ’t Hooft anomaly

The charge-q Schwinger model is the (1 + 1)-dimensional quantum electrodynamics (QED) with a charge-q Dirac fermion. It has the ℤq 1-form symmetry and also enjoys the ℤq chiral symmetry in the chiral limit, and there is a mixed ’t Hooft anomaly between those symmetries. We numerically study the charge-q Schwinger model in the lattice Hamiltonian formulation using the density-matrix renormalization group (DMRG). When applying DMRG, we map the Schwinger model to a spin chain with nonlocal interaction via Jordan-Wigner transformation, and we take the open boundary condition instead of the periodic one to make the Hilbert space finite-dimensional. When computing the energy density or chiral condensate, we find that using local operators significantly reduces the boundary effect compared with the computation of corresponding extensive quantities divided by the volume. To discuss the consequence of the ’t Hooft anomaly, we carefully treat the renormalization of the chiral condensates, and then we confirm that Wilson loops generate the discrete chiral transformations in the continuum limit.

Low-lying excited states of Diphenylpolyenes and its derivatives in singlet fission: A Density Matrix Renormalization Group study

Singlet fission (SF) is a promising mechanism by which the power conversion efficiency (PCE) of the solar cells can be increased. α, ω-Diphenylpolyenes are known to draw research attention due to their fascinating optical and photophysical properties. The low-lying excited states of 1,6-diphenyl-1,3,5-hexatriene (DPH), 1,8-diphenyl-1,3,5,7-octatetraene (DPO), 1,10-diphenyl-1,3,5,7-decapentaene (DPD) molecules and their derivatives are calculated within Pariser–Parr–Pople(PPP) model Hamiltonian implementing Density Matrix Renormalization Group (DMRG) technique. The calculations reveal that all three molecules are promising candidates for SF mechanism. Excited state energies in singlet subspace have been calculated for 1,6-diphenyl-1,3,5-hexatriene (DPH) comprising 18 carbon atoms within exact diagonalization method which are in excellent agreement with results obtained in DMRG technique. Moreover, calculations on α, ω-diphenyl-μ, ν-dicyano oligoenes (DPDCs) show with increasing chain length, these derivatives support endoergic to isoergic SF

Neutral excitations of quantum Hall states: A density matrix renormalization group study

We use the dynamical structure factors of the quantum Hall states at $\ensuremath{\nu}=1/3$ and $1/2$ in the lowest Landau level to study their excitation spectrum. Using the density matrix renormalization group in combination with the time-dependent variational principle on an infinite cylinder geometry, we extract the low-energy properties. At $\ensuremath{\nu}=1/3$, a sharp magnetoroton mode and the two-roton continuum are present and the finite-size effects can be understood using the fractional charge of the quasiparticle. At $\ensuremath{\nu}=1/2$, we find low-energy modes with linear dispersion and the static structure factor $\overline{s}(q)\ensuremath{\sim}{(q\ensuremath{\ell})}^{3}$ in the limit $q\ensuremath{\ell}\ensuremath{\rightarrow}0$. The properties of these modes agree quantitatively with the predictions of the composite-fermion theory placed on the infinite cylinder.

Skyrmion superconductivity: DMRG evidence for a topological route to superconductivity

It was recently suggested that the topology of magic-angle twisted bilayer graphene's (MATBG) flat bands could provide a novel mechanism for superconductivity distinct from both weakly-coupled BCS theory and the $d$-wave phenomenology of the high-$T_c$ cuprates. In this work, we examine this possibility using a density matrix renormalization group (DMRG) study of a model which captures the essential features of MATBG's symmetry and topology. Using large scale cylinder-DMRG calculations to obtain the ground state and its excitations as a function of the electron doping, we find clear evidence for superconductivity driven by the binding of electrons into charge-$2e$ skyrmions. Remarkably, this binding is observed even in the regime where the unscreened Coulomb repulsion is by-far the largest energy scale, demonstrating the robustness of this topological, all-electronic pairing mechanism.

Quantum Spin Liquid Phase in the Shastry-Sutherland Model Detected by an Improved Level Spectroscopic Method

We study the spin-1/2 two-dimensional Shastry–Sutherland spin model by exact diagonalization of clusters with periodic boundary conditions, developing an improved level spectroscopic technique using energy gaps between states with different quantum numbers. The crossing points of some of the relative (composite) gaps have much weaker finite-size drifts than the normally used gaps defined only with respect to the ground state, thus allowing precise determination of quantum critical points even with small clusters. Our results support the picture of a spin liquid phase intervening between the well-known plaquette-singlet and antiferromagnetic ground states, with phase boundaries in almost perfect agreement with a recent density matrix renormalization group study, where much larger cylindrical lattices were used [J. Yang et al., Phys. Rev. B 105, L060409 (2022)]. The method of using composite low-energy gaps to reduce scaling corrections has potentially broad applications in numerical studies of quantum critical phenomena.

Density-matrix renormalization-group study for a two-dimensional lattice-gas on the Ih-ice prism surface

The phase transition temperature of a two-dimensional (2D) lattice-gas model for the Ih-ice prism surface ((1010) surface on a wurtzite crystal structure) is calculated using the density-matrix renormalization-group (DMRG) method. Since the unit cell on the prism surface contains four atoms without inversion symmetry, the asymmetric version of the DMRG is required to obtain a precise value of the phase transition temperature. The effective bond energy on the surface is obtained by comparing the phase transition temperature with the faceting transition temperature observed for a real ice crystal. Using the effective bond energy, the temperature dependence of the coverage on sub-lattice sites is calculated. The surface tensions on the (0001) surface (the basal plane) and the prism plane are also calculated. The surface tension of the basal plane for the ice/water interface agrees well with the recent calculated values obtained by large scale molecular dynamics.

The case of SU(3) criticality in spin-2 chains

It was proposed in [(https://doi.org/10.1103/PhysRevLett.114.145301){Chen et al., Phys. Rev. Lett. $\mathbf{114}$, 145301 (2015)}] that spin-2 chains display an extended critical phase with enhanced SU$(3)$ symmetry. This hypothesis is highly unexpected for a spin-2 system and, as we argue, would imply an unconventional mechanism for symmetry emergence. Yet, the absence of convenient critical points for renormalization group perturbative expansions, allied with the usual difficulty in the convergence of numerical methods in critical or small-gapped phases, renders the verification of this hypothetical SU$(3)$-symmetric phase a non-trivial matter. By tracing parallels with the well-understood phase diagram of spin-1 chains and searching for signatures robust against finite-size effects, we draw criticism on the existence of this phase. We perform non-Abelian density matrix renormalization group studies of multipolar static correlation function, energy spectrum scaling, single-mode approximation, and entanglement spectrum to shed light on the problem. We determine that the hypothetical SU$(3)$ spin-2 phase is, in fact, dominated by ferro-octupolar correlations and also observe a lack of Luttinger-liquid-like behavior in correlation functions that suggests that is perhaps not critical. We further construct an infinite family of spin-$S$ systems with similar ferro-octupolar-dominated quasi-SU$(3)$-like phenomenology; curiously, we note that the spin-3 version of the problem is located in a subspace of exact G$_2$ symmetry, making this a point of interest for search of Fibonacci topological properties in magnetic systems.

Pair-density-wave in the strong coupling limit of the Holstein-Hubbard model

A pair-density-wave (PDW) is a superconducting state with an oscillating order parameter. A microscopic mechanism that can give rise to it has been long sought but has not yet been established by any controlled calculation. Here we report a density-matrix renormalization-group (DMRG) study of an effective t-J-V model, which is equivalent to the Holstein-Hubbard model in a strong-coupling limit, on long two-, four-, and six-leg triangular cylinders. While a state with long-range PDW order is precluded in one dimension, we find strong quasi-long-range PDW order with a divergent PDW susceptibility as well as the spontaneous breaking of time-reversal and inversion symmetries. Despite the strong interactions, the underlying Fermi surfaces and electron pockets around the K and {K}^{prime} points in the Brillouin zone can be identified. We conclude that the state is valley-polarized and that the PDW arises from intra-pocket pairing with an incommensurate center of mass momentum. In the two-leg case, the exponential decay of spin correlations and the measured central charge c ≈ 1 are consistent with an unusual realization of a Luther-Emery liquid.

Physical properties of the massive Schwinger model from the nonperturbative functional renormalization group

We investigate the massive Schwinger model in $d=1+1$ dimensions using bosonization and the nonperturbative functional renormalization group. In agreement with previous studies we find that the phase transition, driven by a change of the ratio $m/e$ between the mass and the charge of the fermions, belongs to the two-dimensional Ising universality class. The temperature and vacuum angle dependence of various physical quantities (chiral density, electric field, entropy density) are also determined and agree with results obtained from density matrix renormalization group studies. Screening of fractional charges and deconfinement occur only at infinite temperature. Our results exemplify the possibility to obtain virtually all physical properties of an interacting system from the functional renormalization group.