Finite-size Density-matrix Renormalization Group Research Articles

Density-wave-ordered phases of Rydberg atoms on a honeycomb lattice.

Rydberg atom arrays have recently emerged to be a promising platform for the exploration of exotic quantum phases of matter and quantum phenomena. In this work, we map out the ground-state phase diagram of Rydberg atoms on a honeycomb lattice as a function of the Rydberg blockade radius and the laser detuning by performing large-scale finite-size density matrix renormalization group simulations. Apart from a featureless disordered phase, we find five other intricate long-range density-wave-ordered phases within a relatively wide parameter space. The properties of these quantum phases are analyzed by calculating their Rydberg excitation profiles and static structure factors. In addition, a continuous quantum phase transition belonging to the (2+1)-dimensional Ising universality class is explored by a standard finite-size scaling analysis. Our work implies some different physics, such as the possible nontrivial quantum phase transitions and a highly degenerate string ordered phase, that a honeycomb geometry could bring to the Rydberg system and serves as a numerical guide for possible real experiments.

Quantum entanglement and criticality in a one-dimensional deconfined quantum critical point.

We investigate the ground-state quantum entanglement in a one-dimensional incarnation of deconfined quantum critical point by making use of the finite-size density matrix renormalization group method. We observe two distinct behaviors of two-site entanglement calculated on odd and even bonds, and the difference O_{E} is shown to obey conventional scaling relations for order parameters. Accurate deconfined critical point and associated critical exponents are numerically extracted from finite-size scaling analyses. We further notice a close similarity between O_{E} and the valence-bond-solid order parameter and same observations are also obtained for quantum coherence and trace distance. Furthermore, the deconfined critical point is suggested to possess rich quantum entanglement other than the two-site entanglement from the residual entanglement perspective. Our work explores the critical characteristics of the one-dimensional deconfined quantum critical point from the quantum information aspect and provides insights for its ground-state entanglement structure.

Fidelity as a probe for a deconfined quantum critical point

Deconfined quantum critical point was proposed as a second-order quantum phase transition between two broken symmetry phases beyond the Landau-Ginzburg-Wilson paradigm. However, numerical studies cannot completely rule out a weakly first-order transition because of strong violations of finite-size scaling. We demonstrate that the fidelity is a simple probe to study deconfined quantum critical point. We study the ground-state fidelity susceptibility close to the deconfined quantum critical point in a spin chain using the large-scale finite-size density matrix renormalization group method. We find that the finite-size scaling of the fidelity susceptibility obeys the conventional scaling behavior for continuous phase transitions, supporting the deconfined quantum phase transition is continuous. We numerically determine the deconfined quantum critical point and the associated correlation length critical exponent from the finite-size scaling theory of the fidelity susceptibility. Our results are consistent with recent results obtained directly from the matrix product states for infinite-size lattices using others observables. Our work provides a useful probe to study critical behaviors at deconfined quantum critical point from the concept of quantum information.

Entanglement properties of the Haldane phases: A finite system-size approach

We study the bond-alternating Heisenberg model using the finite-size density-matrix renormalization group (DMRG) technique and analytical arguments based on the matrix product state, where we pay particular attention to the boundary-condition dependence on the entanglement spectrum of the system. We show that, in the antiperiodic boundary condition (APBC), the parity quantum numbers are equivalent to the topological invariants characterizing the topological phases protected by the bond-centered inversion and $\pi$ rotation about $z$ axis. We also show that the odd parity in the APBC, which characterizes topologically nontrivial phases, can be extracted as a two-fold degeneracy in the entanglement spectrum even with finite system size. We then determine the phase diagram of the model with the uniaxial single-ion anisotropy using the level spectroscopy method in the DMRG technique. These results not only suggest the detectability of the symmetry protected topological (SPT) phases via general twisted boundary conditions but also provide a useful and precise numerical tool for discussing the SPT phases in the exact diagonalization and DMRG techniques.

Hard-core bosons in a zig-zag optical superlattice

We study a system of hard-core bosons at half-filling in a one-dimensional optical superlattice. The bosons are allowed to hop to nearest and next-nearest neighbor sites producing a zig-zag geometry and we obtain the ground state phase diagram as a function of microscopic parameters using the finite-size density matrix renormalization group (FS-DMRG) method. Depending on the sign of the next-nearest neighbor hopping and the strength of the superlattice potential the system exhibits three different phases, namely the bond-order (BO) solid, the superlattice induced Mott insulator (SLMI) and the superfluid (SF) phase. When the signs of both hopping amplitudes are the same (the "unfrustrated" case), the system undergoes a transition from the SF to the SLMI at a non-zero value of the superlattice potential. On the other hand, when the two amplitudes differ in sign (the "frustrated" case), the SF is unstable to switching on a superlattice potential and also exists only up to a finite value of the next nearest neighbor hopping. This part of the phase diagram is dominated by the BO phase which breaks translation symmetry spontaneously even in the absence of the superlattice potential and can thus be characterized by a bond order parameter. The transition from BO to SLMI appears to be first order.

Quantum phases of ultracold bosonic atoms in a one-dimensional optical superlattice

We analyze various quantum phases of ultracold bosonic atoms in a periodic one dimensional optical superlattice. Our studies have been performed using the finite size density matrix renormalization group (FS-DMRG) method in the framework of the Bose-Hubbard model. Calculations have been carried out for a wide range of densities and the energy shifts due to the superlattice potential. At commensurate fillings, we find the Mott insulator and the superfluid phases as well as Mott insulators induced by the superlattice. At a particular incommensurate density, the system is found to be in the superfluid phase coexisting with density oscillations for a certain range of parameters of the system.

Density-Matrix Renormalization Group studies of mixture of two different ultracold bosonic atoms

We investigate the ground state phase diagram for a two species Bose mixture in a one dimensional optical lattice using the finite size density matrix renormalization group (FSDMRG) method. We present our result for different combinations of inter and intra-species repulsion strengths with a commensurate filling factor. We obtain a superfluid (SF) to Mott insulator (MI) transition when the inter species interaction term is less than the intra-species interaction term. However, when the former is slightly greater than the latter we find that the two different species reside in spatially separate regions.

Phase separation in a two-species Bose mixture

We study the ground state quantum phase diagram for a two species Bose mixture in a one-dimensional optical lattice using the finite size density matrix renormalization group(FSDMRG) method. We discuss our results for different combinations of inter and intra species interaction strengths with commensurate and incommensurate fillings of the bosons. The phases we have obtained are superfluid, Mott insulator and a novel phase separation, where different species reside in spatially separate regions. The spatially separated phase is further classified into phase separated superfluid(PS-SF) and Mott insulator(PS-MI). The phase separation appears for all the fillings we have considered, whenever the inter-species interaction is slightly larger than the intra-species interactions.

Superfluid, Mott-insulator, and mass-density-wave phases in the one-dimensional extended Bose-Hubbard model

We use the finite-size density-matrix-renormalization-group (FSDMRG) method to obtain the phase diagram of the one-dimensional ($d = 1$) extended Bose-Hubbard model for density $\rho = 1$ in the $U-V$ plane, where $U$ and $V$ are, respectively, onsite and nearest-neighbor interactions. The phase diagram comprises three phases: Superfluid (SF), Mott Insulator (MI) and Mass Density Wave (MDW). For small values of $U$ and $V$, we get a reentrant SF-MI-SF phase transition. For intermediate values of interactions the SF phase is sandwiched between MI and MDW phases with continuous SF-MI and SF-MDW transitions. We show, by a detailed finite-size scaling analysis, that the MI-SF transition is of Kosterlitz-Thouless (KT) type whereas the MDW-SF transition has both KT and two-dimensional-Ising characters. For large values of $U$ and $V$ we get a direct, first-order, MI-MDW transition. The MI-SF, MDW-SF and MI-MDW phase boundaries join at a bicritical point at ($U, V) = (8.5 \pm 0.05, 4.75 \pm 0.05)$.