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By using Gutzwiller projected fermionic wave functions and variational Monte Carlo technique, we study the spin-1/2 Heisenberg model with the first-neighbor (J1), second-neighbor (J2), and additional scalar chiral interaction JχSi.(Sj×Sk) on the triangular lattice. In the nonmagnetic phase of the J1−J2 triangular model with 0.08≲J2/J1≲0.16, recent density-matrix renormalization group (DMRG) studies [Zhu and White, Phys. Rev. B 92, 041105(R) (2015) and Hu, Gong, Zhu, and Sheng, Phys. Rev. B 92, 140403(R) (2015)] find a possible gapped spin liquid with the signal of a competition between a chiral and a Z2 spin liquid. Motivated by the DMRG results, we consider the chiral interaction JχSi.(Sj×Sk) as a perturbation for this nonmagnetic phase. We find that with growing Jχ, the gapless U(1) Dirac spin liquid, which has the best variational energy for Jχ=0, exhibits the energy instability towards a gapped spin liquid with nontrivial magnetic fluxes and nonzero chiral order. We calculate topological Chern number and ground-state degeneracy, both of which identify this flux state as the chiral spin liquid with fractionalized Chern number C=1/2 and twofold topological degeneracy. Our results indicate a positive direction to stabilize a chiral spin liquid near the nonmagnetic phase of the J1−J2 triangular model. [ABSTRACT FROM AUTHOR]

We study the interacting bosons in topological Hofstadter bands with Chern number two. Using exact diagonalization, we demonstrate that the bosonic integer quantum Hall (BIQH) state emerges at integer boson filling factor ν=1 of the lowest Chern band with evidence including a robust spectrum gap and quantized topological Hall conductance two. Moreover, the robustness of BIQH state against different interactions and next-nearest-neighbor hopping is investigated. The strong nearest-neighbor interaction would favor a charge density wave. When the on-site interaction decreases, the BIQH state undergoes a continuous transition into a superfluid state. Without next-nearest-neighbor hopping, the ground state is possibly in a metallic Fermi-liquid-like phase. [ABSTRACT FROM AUTHOR]

By using the variational Monte Carlo technique, we study the spin-1/2] XXZ antiferromagnetic model (with easy-plane anisotropy) on the kagome lattice, A class of Gutzwiller projected fermionic states with a spin Jastrow factor is considered to describe either spin liquids [with (7(1) or Z2 symmetry] or magnetically ordered phases [with q = (0,0) or q = (4π/ 3,0)]. We find that the magnetic states are not stable in the thermodynamic limit. Moreover, there is no energy gain to break the gauge symmetry from (7(1) to Z2 within the spin-liquid states, as previously found in the Heisenberg model. The best variational wave function is therefore the (7(1) Dirac state, supplemented by the spin Jastrow factor. Furthermore, a vanishing 5 = 2 spin gap is obtained at the variational level, in the whole regime from the XY to the Heisenberg model. [ABSTRACT FROM AUTHOR]

The kagome spin-½ systems have attracted intensive attention in recent years as the primary candidate for hosting different gapped spin liquids (SLs). To uncover the nature of the novel quantum phase transition between the SL states, we study a minimum XY model with the nearest-neighbor (NN) (Jxy), the second-NN, and the third-NN couplings (J2xy=J3xy=J'xy). We identify the time-reversal-symmetry-broken chiral SL (CSL) with the turn on of a small perturbation J'xy~0.06Jxy, which is fully characterized by the fractionally quantized topological Chern number and the conformal edge spectrum as the ?=1/2 fractional quantum Hall state. Interestingly, the NN XY model (J'xy=0) is shown to be a critical SL state adjacent to the CSL, characterized by the gapless spin singlet and spin triplet excitations. The quantum phase transition from the CSL to the gapless critical SL is driven by the collapsing of the neutral (spin singlet) excitation gap. The effect of the NN spin-z coupling Jz is also studied, which leads to a quantum phase diagram with an extended regime for the gapless SL. [ABSTRACT FROM AUTHOR]

Topological quantum states with non-Abelian Fibonacci anyonic excitations are widely sought after for the exotic fundamental physics they would exhibit, and for universal quantum computing applications. The fractional quantum Hall (FQH) state at a filling factor of ν = 12/5 is a promising candidate; however, its precise nature is still under debate and no consensus has been achieved sofar. Here, we investigate the nature of the FQH ν= 13/5 state and its particle-hole conjugate state at 12/5 with the Coulomb interaction, and we address the issue of possible competing states. Based on a large-scale density-matrix renormalization group calculation in spherical geometry, we present evidence that the essential physics of the Coulomb ground state (GS) at ν = 13/5 and 12/5 is captured by the k = 3 parafermion Read-Rezayi state (RR3), including a robust excitation gap and the topological fingerprint from the entanglement spectrum and topological entanglement entropy. Furthermore, by considering the infinite-cylinder geometry (topologically equivalent to torus geometry), we expose the non-Abelian GS sector corresponding to a Fibonacci anyonic quasiparticle, which serves as a signature of the RR3 state at 13/5 and 12/5 filling numbers. [ABSTRACT FROM AUTHOR]

We investigate the extended Heisenberg model on the kagome lattice by using Gutzwiller projected fermionic states and the variational Monte Carlo technique. In particular, when both second- and third-neighbor superexchanges are considered, we find that a gapped spin liquid described by nontrivial magnetic fluxes and long-range chiral-chiral correlations is energetically favored compared to the gapless U(l) Dirac state. Furthermore, the topological Chern number, obtained by integrating the Berry curvature, and the degeneracy of the ground state, by constructing linearly independent states, lead us to identify this flux state as the chiral spin liquid with a C = 1/2 fractionalized Chern number. [ABSTRACT FROM AUTHOR]

The quantum spin Hall (QSH) effect is known to be unstable to perturbations violating time-reversal symmetry. We show that creating a narrow ferromagnetic region near the edge of a QSH sample can push one of the counterpropagating edge states to the inner boundary of the ferromagnetic region and leave the other at the outer boundary, without changing their spin polarizations and propagation directions. Since the two edge states are spatially separated into different "lanes," the QSH effect becomes robust against symmetry-breaking perturbations. [ABSTRACT FROM AUTHOR]

Inspired by the recent theoretical discovery of robust fractional topological phases without a magnetic field, we search for the non-Abelian quantum Hall effect in lattice models with topological flat bands. Through extensive numerical studies on the Haldane model with three-body hard-core bosons loaded into a topological flat band, we find convincing numerical evidence of a stable v = 1 bosonic non-Abelian quantum Hall effect, with the characteristic threefold quasidegeneracy of ground states on a torus, a quantized Chem number, and a robust spectrum gap. Moreover, the spectrum for two-quasihole states also shows a finite energy gap, with the number of states in the lower-energy sector satisfying the same counting rule as the Moore-Read Pfaffian state. [ABSTRACT FROM AUTHOR]

We demonstrate the existence of robust bulk extended states in the disordered Kane-Mele model with vertical and horizontal Zeeman fields in the presence of a large Rashba coupling. The phase diagrams are mapped out by using level statistics analysis and computations of the localization length and spin-Chern numbers C±. C± are protected by the finite energy and spin mobility gaps. The latter stay open for arbitrarily large vertical Zeeman fields, or for horizontal Zeeman fields below a critical strength or at moderate disorder. In such cases, a change of C± is necessarily accompanied by the closing of the mobility gap at the Fermi level. The numerical simulations reveal sharp changes in the quantized values of C± when crossing the regions of bulk extended states, indicating that the topological nature of the extended states is indeed linked to the spin-Chern numbers. For large horizontal Zeeman fields, the spin mobility gap closes at strong disorder, prompting a change in the quantized spin-Chern numbers without a closing of the energy mobility gap. [ABSTRACT FROM AUTHOR]

Recent proposals of topological flat band models have provided a new route to realize the fractional quantum Hall effect without Landau levels. We study hard-core bosons with short-range interactions in two representative topological flat band models, one of which is the well-known Haldane model (but with different parameters). We demonstrate that fractional quantum Hall states emerge with signatures of an even number of quasidegenerate ground states on a torus and a robust spectrum gap separating these states from the higher energy spectrum. We also establish quantum phase diagrams for the filling factor 1/2 and illustrate quantum phase transitions to other competing symmetry-breaking phases. [ABSTRACT FROM AUTHOR]

The quantum spin Hall (QSH) state of matter is usually considered to be protected by time-reversal (TR) symmetry. We investigate the fate of the QSH effect in the presence of the Rashba spin-orbit coupling and an exchange field, which break both inversion and TR symmetries. It is found that the QSH state characterized by nonzero spin Chern numbers C± = ±1 persists when the TR symmetry is broken. A topological phase transition from the TR-symmetry-broken QSH phase to a quantum anomalous Hall phase occurs at a critical exchange field, where the bulk band gap just closes. It is also shown that the transition from the TR-symmetry-broken QSH phase to an ordinary insulator state cannot happen without closing the band gap. [ABSTRACT FROM AUTHOR]

We study the quantum phase diagram of electrons on kagome lattice with half-filled lowest flat bands by considering the antiferromagnetic Heisenberg interaction J, and short-range Coulomb interaction V. In the weak J regime, we identify a fully spin-polarized phase. The presence of finite V drives a spontaneous chiral current, which makes the system an orbital Chern insulator by contributing an orbital magnetization. Such an out-of-plane orbital magnetization allows the presence of a Chern insulating phase independent of the spin orientation in contrast to the spin-orbit coupling induced Chern insulator that disappears with in-plane ferromagnetism constrained by symmetry. Such a symmetry difference provides a criterion to distinguish the physical origin of topological responses in kagome systems. The orbital Chern insulator is robust against small coupling J. By further increasing J, we find that the ferromagnetic topological phase is suppressed, which first becomes partially polarized and then enters a nonmagnetic phase with spin and charge nematicity. The frustrated flat band allows the spin and Coulomb interaction to play an essential role in determining the quantum phases. [ABSTRACT FROM AUTHOR]

We revisit the effects of the Hubbard repulsion on quantum spin Hall effects (QSHE) in two-dimensional quantum lattice models. We present both unbiased exact diagonalization and density-matrix renormalization group simulations with numerical evidence for a continuous quantum phase transition (CQPT) separating QSHE from the topologically trivial antiferromagnetic phase. Our numerical results suggest that the nature of CQPT exhibits distinct finite-size scaling behaviors, which may be consistent with either Ising or XY universality classes for different time-reversal symmetric QSHE systems. [ABSTRACT FROM AUTHOR]

We study the spin-1/2 Heisenberg model on the triangular lattice with the nearest-neighbor J1 > 0, the next-nearest-neighobr J2 > 0 Heisenberg interactions, and the additional scalar chiral interaction Jχ (Si × Sj) · Sk for the three spins in all the triangles using large-scale density matrix renormalization group calculation on cylinder geometry. With increasing J2 (J2/J1 ≤ 0.3) and Jχ (Jχ/J1 ≤ 1.0) interactions, we establish a quantum phase diagram with the magnetically ordered 120°, stripe, and noncoplanar tetrahedral phase. In between these magnetic order phases, we find a chiral spin liquid (CSL) phase, which is identified as a ν = 1/2 bosonic fractional quantum Hall state with possible spontaneous rotational symmetry breaking. By switching on the chiral interaction, we find that the previously identified spin liquid in the J1 - J2 triangular model (0.08 ≾ J2/J1 ≾ 0.15) shows a phase transition to the CSL phase at very small Jχ. We also compute the spin triplet gap in both spin liquid phases, and our finite-size results suggest a large gap in the odd topological sector but a small or vanishing gap in the even sector. We discuss the implications of our results on the nature of the spin liquid phases. [ABSTRACT FROM AUTHOR]

We study the ground-state phase diagram of the quantum spin-1/2 Heisenberg model on the kagome lattice with first- (J1<0), second- (J2<0), and third-neighbor interactions (Jd>0) by means of analytical low-energy field theory and numerical density-matrix renormalization group (DMRG) studies. The results offer a consistent picture of the Jd-dominant regime in terms of three sets of spin chains weakly coupled by the ferromagnetic interchain interactions J1,2. When either J1 or J2 is much stronger than the other one, the model is found to support one of two cuboctohedral phases, cuboc1, and cuboc2. These cuboc states host noncoplanar long-ranged magnetic order and possess finite scalar spin chirality. However, in the compensated regime J1≃J2, a valence bond crystal phase emerges between the two cuboc phases. We find excellent agreement between an analytical theory based on coupled spin chains and unbiased DMRG calculations, including at a very detailed level of comparison of the structure of the valence bond crystal state. To our knowledge, this is the first such comprehensive understanding of a highly frustrated two-dimensional quantum antiferromagnet. We find no evidence of either the one-dimensional gapless spin liquid or the chiral spin liquids, which were previously suggested by parton mean-field theories. [ABSTRACT FROM AUTHOR]

We study the spin-½ Heisenberg model on the triangular lattice with antiferromagnetic first- (J1) and second- (J2) nearest-neighbor interactions using density matrix renormalization group. By studying the spin correlation function, we find a 120° magnetic order phase for J2 ≲ 0.07J1 and a stripe antiferromagnetic phase for J2 ≳ 0.15J1. Between these two phases, we identify a spin-liquid region characterized by exponential decaying spin and dimer correlations, as well as large spin singlet and triplet excitation gaps on finite-size systems. We find two near degenerating ground states with distinct properties in two sectors, which indicates more than one spin-liquid candidate in this region. While the sector with spinons is found to respect time reversal symmetry, the even sector without spinons breaks such a symmetry for finite-size systems. Furthermore, we detect the signature of the fractionalization by following the evolution of different ground states with inserting spin flux into the cylinder system. Moreover, by tuning the anisotropic bond coupling, we explore the nature of the spin-liquid phase and find the optimal parameter region for gapped Z2 spin liquids. [ABSTRACT FROM AUTHOR]

We study the quantum phase diagram of the spin-1/2 Heisenberg model on the kagome lattice with first-, second-, and third-neighbor interactions J1,J2, and J3 by means of density matrix renormalization group. For small J2 and J3, this model sustains a time-reversal invariant quantum spin-liquid phase. With increasing J2 and J3, we find in addition a q=(0,0) Néel phase, a chiral spin-liquid phase, an apparent valence-bond crystal phase, and a complex noncoplanar magnetically ordered state with spins forming the vertices of a cuboctahedron known as a cuboc1 phase. Both the chiral spin liquid and cuboc1 phase break time-reversal symmetry in the sense of spontaneous scalar spin chirality. We show that the chiralities in the chiral spin liquid and cuboc1 are distinct, and that these two states are separated by a strong first-order phase transition. The transitions from the chiral spin liquid to both the q=(0,0) phase and to time-reversal symmetric spin liquid, however, are consistent with continuous quantum phase transitions. [ABSTRACT FROM AUTHOR]

We predict the emergence of a state of matter with intertwined ferromagnetism, charge order, and topology in fractionally filled moiré superlattice bands. Remarkably, these quantum anomalous Hall crystals exhibit a quantized integer Hall conductance that is different than expected from the filling and Chern number of the band. Microscopic calculations show that this phase is robustly favored at half-filling (ν=1/2) at larger twist angles of the twisted semiconductor bilayer tMoTe&#95;{2}.

The square-lattice Hubbard and closely related t-J models are considered as basic paradigms for understanding strong correlation effects and unconventional superconductivity (SC). Recent large-scale density matrix renormalization group simulations on the extended t-J model have identified d-wave SC on the electron-doped side (with the next-nearest-neighbor hopping t&#95;{2}>0) but a dominant charge density wave (CDW) order on the hole-doped side (t&#95;{2}<0), which is inconsistent with the SC of hole-doped cuprate compounds. We re-examine the ground-state phase diagram of the extended t-J model by employing the state-of-the-art density matrix renormalization group calculations with much enhanced bond dimensions, allowing more accurate determination of the ground state. On six-leg cylinders, while different CDW phases are identified on the hole-doped side for the doping range δ=1/16-1/8, a SC phase emerges at a lower doping regime, with algebraically decaying pairing correlations and d-wave symmetry. On the wider eight-leg systems, the d-wave SC also emerges on the hole-doped side at the optimal 1/8 doping, demonstrating the winning of SC over CDW by increasing the system width. Our results not only suggest a new path to SC in general t-J model through weakening the competing charge orders, but also provide a unified understanding on the SC of both hole- and electron-doped cuprate superconductors.

Unravelling competing orders emergent in doped Mott insulators and their interplay with unconventional superconductivity is one of the major challenges in condensed matter physics. To explore the possible superconducting state in a doped Mott insulator, we study the square-lattice t-J model with both the nearest-neighbor and next-nearest-neighbor electron hoppings and spin interactions. By using the state-of-the-art density matrix renormalization group calculation with imposing charge U(1) and spin SU(2) symmetries on the six-leg cylinders, we establish a quantum phase diagram including three phases: a stripe charge density wave phase, a superconducting phase without static charge order, and a superconducting phase coexistent with a weak charge stripe order. Crucially, we demonstrate that the superconducting phase has a power-law pairing correlation that decays much slower than the charge density and spin correlations, which is a quasi-1D descendant of the uniform d-wave superconductor in two dimensions. These findings reveal that enhanced charge and spin fluctuations with optimal doping is able to produce robust d-wave superconductivity in doped Mott insulators, providing a foundation for connecting theories of superconductivity to models of strongly correlated systems.

We study the spin-1/2 Heisenberg model on the square lattice with first- and second-neighbor antiferromagnetic interactions J(1) and J(2), which possesses a nonmagnetic region that has been debated for many years and might realize the interesting Z(2) spin liquid. We use the density matrix renormalization group approach with explicit implementation of SU(2) spin rotation symmetry and study the model accurately on open cylinders with different boundary conditions. With increasing J(2), we find a Néel phase and a plaquette valence-bond (PVB) phase with a finite spin gap. From the finite-size scaling of the magnetic order parameter, we estimate that the Néel order vanishes at J(2)/J(1)≃0.44. For 0.5

It is well known that the topological phenomena with fractional excitations, the fractional quantum Hall effect, will emerge when electrons move in Landau levels. Here we show the theoretical discovery of the fractional quantum Hall effect in the absence of Landau levels in an interacting fermion model. The non-interacting part of our Hamiltonian is the recently proposed topologically non-trivial flat-band model on a checkerboard lattice. In the presence of nearest-neighbouring repulsion, we find that at 1/3 filling, the Fermi-liquid state is unstable towards the fractional quantum Hall effect. At 1/5 filling, however, a next-nearest-neighbouring repulsion is needed for the occurrence of the 1/5 fractional quantum Hall effect when nearest-neighbouring repulsion is not too strong. We demonstrate the characteristic features of these novel states and determine the corresponding phase diagram.

We study a spin-1/2 system with Heisenberg plus ring exchanges on a four-leg triangular ladder using the density matrix renormalization group and Gutzwiller variational wave functions. Near an isotropic lattice regime, for moderate to large ring exchanges we find a spin Bose-metal phase with a spinon Fermi sea consisting of three partially filled bands. Going away from the triangular towards the square lattice regime, we find a staggered dimer phase with dimers in the transverse direction, while for small ring exchanges the system is in a featureless rung phase. We also discuss parent states and a possible phase diagram in two dimensions.