First-order quantum Hall to Wigner crystal phase transition on a triangular lattice: An infinite density matrix renormalization group study

At strong repulsion, the triangular-lattice Hubbard model is described by s=1/2 spins with nearest-neighbor antiferromagnetic Heisenberg interactions and exhibits conventional 120° order. Using the infinite density matrix renormalization group and exact diagonalization, we study the effect of the additional four-spin interactions naturally generated from the underlying Mott-insulator physics of electrons as the repulsion decreases. Although these interactions have historically been connected with a gapless ground state with emergent spinon Fermi surface, we find that, at physically relevant parameters, they stabilize a chiral spin liquid (CSL) of Kalmeyer-Laughlin (KL) type, clarifying observations in recent studies of the Hubbard model. We then present a self-consistent solution based on a mean-field rewriting of the interaction to obtain a Hamiltonian with similarities to the parent Hamiltonian of the KL state, providing a physical understanding for the origin of the CSL.

We report the symmetrized density matrix renormalization group (DMRG) study of neutral and doped oligomers of poly-para-phenylene (PPP) system within an extended Hubbard model. Model parameters are determined by comparing the existing results for an interacting small system. We compute a number of properties in the ground state as well as in the one-photon, two-photon and triplet states to completely characterize these states. Bond-order studies show that the lowest two-photon state corresponds to a localized excitation while one-photon and triplet excitations are extended in nature. The bipolaronic state shows clear evidence for charge separation and disproportionation into two polarons. We find that the extended nature of one-photon and triplet states of the neutral system are very similar to those of the bipolaronic ground states.

We study orbital diamagnetism at zero temperature in (2 + 1)-dimensional Dirac fermions with a short-range interaction which exhibits a quantum phase transition to a charge density wave (CDW) phase. We introduce orbital magnetic fields into spinless Dirac fermions on the π-flux square lattice, and analyze them by using infinite density matrix renormalization group. It is found that the diamagnetism remains intact in the Dirac semimetal regime, while it is monotonically suppressed in the CDW regime. Around the quantum critical point of the CDW phase transition, we find a scaling behavior of the diamagnetism characteristic of the chiral Ising universality class. Besides, the scaling analysis implies that the robust orbital diamagnetism at weak magnetic fields in a Dirac semimetal regime would hold not only in our model but also in other interacting Dirac fermion systems as long as scaling regions are wide enough. The scaling behavior may also be regarded as a quantum, magnetic analogue of the critical Casimir effect which has been widely studied for classical phase transitions.

We investigate the quantum many-body instabilities of the extended Hubbard model for spinless fermions on the honeycomb lattice with repulsive nearest-neighbor and 2nd nearest-neighbor density-density interactions. Recent exact diagonalization and infinite density matrix renormalization group results suggest that a putative topological Mott insulator phase driven by the 2nd nearest-neighbor repulsion is suppressed, while other numerically exact approaches support the topological Mott insulator scenario. In the present work, we employ the functional renormalization group (fRG) for correlated fermionic systems. Our fRG results hint at a strong suppression of the scattering processes stabilizing the topological Mott insulator. From analyzing the effects of fermionic fluctuations, we obtain a phase diagram which is the result of the competition of various charge ordering instabilities.

We study the strong odd bond - weak even bond picture by measuring the bond energy and the half-chain entanglement entropy in the one-dimensional Hubbard model. By using the infinite density matrix renormalization group with matrix product operator, we obtain the ground state of the matrix product state. As a function of the bond dimension, the bond energy and the half-chain entanglement entropy support the strong odd bond - weak even bond picture. From the expectation values of the occupation number, we numerically observe that the odd - even effect appears only for the half-filling case with a finite bond dimension. Our results confirm that the matrix product operator method is successful in exploring itinerant fermionic systems.

We investigate the critical behavior of the $S=1/2$ alternating Heisenberg chain using the density matrix renormalization group. The ground-state energy per spin, ${e}_{0},$ and singlet-triplet energy gap $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\Delta}}$ are determined for a range of alternations $\ensuremath{\delta}.$ Our results for the approach of ${e}_{0}$ to the uniform chain limit are well described by $c{\ensuremath{\delta}}^{p},$ with $p\ensuremath{\approx}1.45.$ The singlet-triplet gap is also well described by a power law, with $p\ensuremath{\approx}0.73,$ half of the ${e}_{0}$ power. The renormalization group predictions of power laws with logarithmic corrections can also accurately describe our data provided that a surprisingly large-scale parameter ${\ensuremath{\delta}}_{0}$ is present in the logarithms.

The significant electron-electron interactions that characterize the {\pi}-electrons of graphene nanoribbons (GNRs) necessitate going beyond one-electron tight-binding description. Existing theories of electron-electron interactions in GNRs take into account one electron-one hole interactions accurately but miss higher order effects. We report highly accurate density matrix renormalization group (DMRG) calculations of the ground state electronic structure, the relative energies of the lowest one-photon versus two-photon excitations and the charge gaps in three narrow graphene nanoribbons (GNRs) within the correlated Pariser-Parr-Pople model for {\pi}-conjugated systems. We have employed the symmetrized DMRG method to investigate the zigzag nanoribbon 3-ZGNR and two armchair nanoribbons 6-AGNR and 5-AGNR, respectively. We predict bulk magnetization of the ground state of 3-ZGNR, and a large spin gap in 6-AGNR in their respective thermodynamic limits. Nonzero charge gaps and semiconducting behavior, with moderate to large exciting binding energies are found for all three nanoribbons, in contradiction to the prediction of tight-binding theory. The lowest two-photon gap in 3-ZGNR vanishes in the thermodynamic limit, while this gap is smaller than the one-photon gap in 5-AGNR. However, in 6-AGNR the one-photon gap is smaller than the two-photon gap and it is predicted to be fluorescent.

Using the (dynamical) density-matrix renormalization group method, we study the low-energy physics of three-leg antiferromagnetic Heisenberg model where the periodic boundary conditions are applied in the rung direction. We confirm that the spin excitations are always gapped as long as the intraring couplings form a regular triangle. From precise finite-size-scaling analyses of the spin gap and dimerization order parameter, we also find that the spin gap is collapsed by very small asymmetric modulation of the intraring couplings. Moreover, the dynamical spin structure factors on the intraleg and interleg correlations are calculated. It is demonstrated that the low-lying structure of the interleg spectra is particularly affected by the asymmetric modulation.

We study a magnetic impurity embedded in a correlated electron system using the density-matrix renormalization group method. The correlated electron system is described by the one-dimensional Hubbard model. At half filling, we confirm that the binding energy of the singlet bound state increases exponentially in the weak-coupling regime and decreases inversely proportional to the correlation in the strong-coupling regime. The spin-spin correlation shows an exponential decay with distance from the impurity site. The correlation length becomes smaller with increasing the correlation strength. We find discontinuous reduction of the binding energy and of spin-spin correlations with hole doping. The binding energy is reduced by hole doping; however, it remains of the same order of magnitude as for the half-filled case.

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 investigate the dynamical spin and charge structure factors of the t-t'-J four-leg ladder by using dynamical density-matrix renormalization group. The dynamical charge structure factor along the momentum direction from q=(0,0) to (pi,0) clearly shows low-energy excitations corresponding to the stripe order in hole doping. On the other hand, the stripe order weakens in electron doping, resulting in less low-energy excitations in the charge channel. In spin channel, we find incommensurate spin excitations near q=(pi,pi) forming a hour-glass behavior in hole doping, while in electron doping we find clearly spin-wave-like dispersions starting from q=(pi,pi). Along the (0,0)-(pi,0) direction, the spin excitations are strongly influenced by the stripes in hole doping, resulting in two branches that form a discontinuous behavior in the dispersion. In contrast, the electron-doped systems show a downward shift in energy toward (pi,0).

Correlated-electron theories of superconductivity in layered cuprates often\nstart from the premise of a gapped spin-liquid phase proximate to the\nsuperconducting state. This assumption is justified based on analytical and\nnumerical demonstrations of a superconducting Luther-Emery phase in the doped\n2-leg one-band Hubbard ladder, and the perceived analogy between coupled\nladders and the two dimensional CuO2 layer. We demonstrate from accurate\ndensity matrix renormalization group studies the absence of the superconducting\nLuther-Emery phase in the doped 2-leg three-band ladder consisting of both\ncopper and oxygen, even as the spin gap is large in the undoped three-band\nladder. For realistic oxygen-oxygen hopping and Hubbard repulsion on the oxygen\natoms, density-density rather than pairing correlations are dominant at long\nrange. This result is equally valid whether or not the oxygens outside the\nladder proper, over and above the rung and leg oxygens, are included in the\ncomputation. These results demonstrate the critical importance of oxygen\norbitals, and raise disturbing questions about the applicability of many of the\nexisting correlated-electron theories of superconductivity.\n

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.

We construct a two-dimensional (2D) lattice model that is argued to realize a gapped chiral spin liquid with (Ising) non-Abelian topological order. The building blocks are spin-1/2 two-leg ladders with $SU(2)$-symmetric spin-spin interactions. The two-leg ladders are then arranged on rows and coupled through SU(2)-symmetric interactions between consecutive ladders. The intra-ladder interactions are tuned so as to realize the c = 1/2 Ising conformal field theory, a fact that we establish numerically via Density Matrix Renormalization Group (DMRG) studies. Time-reversal breaking inter-ladder interactions are tuned so as to open a bulk gap in the 2D lattice system. This 2D system supports gapless chiral edge modes with Ising non-Abelian excitations but no charge excitations, in contrast to the Pfaffian non-Abelian fractional quantum Hall state.

Fermions in two-dimensions (2D) when subject to anisotropic spin-dependent hopping can potentially give rise to unusual paired states in {\it unpolarized} mixtures that can behave as non-Fermi liquids. One possibility is a fully paired state with a gap for fermion excitations in which the Cooper pairs remain uncondensed. Such a "Cooper-pair Bose-metal" phase would be expected to have a singular Bose-surface in momentum space. As demonstrated in the context of 2D bosons hopping with a frustrating ring-exchange interaction, an analogous Bose-metal phase has a set of quasi-1D descendent states when put on a ladder geometry. Here we present a density matrix renormalization group (DMRG) study of the attractive Hubbard model with spin-dependent hopping on a two-leg ladder geometry. In our setup, one spin species moves preferentially along the leg direction, while the other does so along the rung direction. We find compelling evidence for the existence of a novel Cooper-pair Bose-metal phase in a region of the phase diagram at intermediate coupling. We further explore the phase diagram of this model as a function of hopping anisotropy, density, and interaction strength, finding a conventional superfluid phase, as well as a phase of paired Cooper pairs with d-wave symmetry, similar to the one found in models of hard-core bosons with ring-exchange. We argue that simulating this model with cold Fermi gases on spin dependent optical lattices is a promising direction for realizing exotic quantum states.