We study quantum phases and phase transitions in a one-dimensional interacting fermion system with a Lieb-Schultz-Mattis (LSM) type anomaly. Specifically, the inversion symmetry enforces any symmetry-preserving gapped ground state of the system to be
a Kitaev chain, following a Lieb-Schultz-Mattis type theorem that we prove. Alternatively, via the Jordan-Wigner transformation, this system describes a spin system whose gapped ground states must break either the inversion or the Ising symmetry associated with fermion parity. We obtain a phase diagram using analytical methods and variational matrix product state simulations, and study the critical behaviors of the quantum phase transitions therein using entanglement entropy, energy variance and finite size scaling of order parameters. In particular, we observe continuous phase transitions between different ordered phases that are beyond the Ginzburg-Landau-Wilson paradigm, in analogy to the deconfined quantum critical points in two spatial dimensions. We show this type of 1D deconfined quantum critical point is described by the Tomonaga-Luttinger liquid theory, and extract the Luttinger parameter and critical exponents. We also identify a gapless phase between two ordered phases, which cannot be described by a U(1) Luttinger liquid.
Moire systems provide a rich platform for studies of strong correlation physics. Recent experiments on hetero-bilayer transition metal dichalcogenide (TMD) Moire systems are exciting in that they manifest a relatively simple model system of an extend
ed Hubbard model on a triangular lattice. Inspired by the prospect of the hetero-TMD Moire systems potential as a solid-state-based quantum simulator, we explore the extended Hubbard model on the triangular lattice using the density matrix renormalization group (DMRG). Specifically, we explore the two-dimensional phase space of the kinetic energy relative to the interaction strength $t/U$ and the further-range interaction strength $V_1/U$. We find competition between Fermi fluid, chiral spin liquid, spin density wave, and charge density wave. In particular, our finding of the optimal further-range interaction for the chiral correlation presents a tantalizing possibility.
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 possible superconductivity state in the doped Mott insulat
or, we study a square-lattice $t$-$J$ model with both the nearest and next-nearest-neighbor electron hoppings and spin Heisenberg interactions. By using the state-of-the-art density matrix renormalization group simulations with imposing charge $U(1)$ and spin $SU(2)$ symmetries on the large-scale 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 decaying 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.
Motivated by the recent proposal of realizing an SU(4) Hubbard model on triangular moire superlattices, we present a DMRG study of an $SU(4)$ spin model obtained in the limit of large repulsion for integer filling $ u_T=1,3$. We retain terms in the $
t/U$ expansion up to $O(frac{t^3}{U^2})$ order, that generates nearest-neighbor exchange $J$, as well as an additional three-site ring exchange term, $K$, which is absent in the SU(2) S=1/2 case. For filling $ u_T=3$, when increasing the three-site ring exchange term $K sim frac{t^3}{U^2}$, we identify three different phases: a spin-symmetric crystal, an $SU(4)_1$ chiral spin liquid (CSL) and a decoupled one dimensional chain (DC) phase. The CSL phase exists at intermediate coupling: $U/t in [11.3,,22.9]$. The sign of $K$ is crucial to stabilizing the CSL and the DC phase. For filling $ u_T=1$ with the opposite sign of $K$, the spin-symmetric crystal phase survives to very large $K$. We propose to search for the CSL phase in moire bilayers. For example, in twisted AB stacked transition metal dichalcogenide (TMD) bilayers, the $SU(4)$ spin is formed by layer pseudospin combined with the real spin (locked to valley). The layer pseudospin carries an electric dipole moment in $z$ direction, thus the CSL is really a dipole-spin liquid, with quantum fluctuations in both the electric moment and magnetic moment . The CSL phase spontaneously breaks the time reversal symmetry and shows a quantum anomalous Hall effect in spin transport and dipole transport. Smoking gun evidence for the CSL could be obtained through measurement of the quantized dipole Hall effect in counter-flow transport.
Motivated by the experiments on the organic compound $(Per)_{2}[Pt(mnt)_{2}]$, we study the ground state of the one-dimensional Kondo lattice model at quarter filling with the density matrix renormalization group method. We show a coupled dimer and b
ond-order-wave (BOW) state in the weak coupling regime for the localized spins and itinerant electrons, respectively. The quantum phase transitions for the dimer and the BOW orders occur at the same critical coupling parameter $J_{c}$, with the opening of a charge gap. The emergence of the combination of dimer and BOW order agrees with the experimental findings of the simultaneous Peierls and spin-Peierls transitions at low temperatures, which provides a theoretical understanding of such phase transition. We also show that the localized spins in this insulating state have quasi-long ranged spin correlations with collinear configurations, which resemble the classical dimer order in the absence of a magnetic order.
We numerically study the three-dimensional (3D) quantum Hall effect (QHE) and magnetothermoelectric transport of Weyl semimetals in the presence of disorder. We obtain a bulk picture that the exotic 3D QHE emerges in a finite range of Fermi energy ne
ar the Weyl points determined by the gap between the $n=-1$ and $n=1$ Landau levels (LLs). The quantized Hall conductivity is attributable to the chiral zeroth LLs traversing the gap, and is robust against disorder scattering for an intermediate number of layers in the direction of the magnetic field. Moreover, we predict several interesting characteristic features of the thermoelectric transport coefficients in the 3D QHE regime, which can be probed experimentally. This may open an avenue for exploring Weyl physics in topological materials.
We investigate the evolution of the Mott insulators in the triangular lattice Hubbard Model, as a function of hole doping $delta$ in both the strong and intermediate coupling limit. Using the density matrix renormalization group (DMRG) method, at lig
ht hole doping $deltalesssim 10%$, we find a significant difference between strong and intermediate couplings. Notably, at intermediate coupling an unusual metallic state emerges, with short ranged spin correlations but long ranged spin-chirality order. Moreover, no clear Fermi surface or wave-vector is observed. These features disappear on increasing interaction strength or on further doping. At strong coupling, the 120 degree magnetic order of the insulating magnet persists for light doping, and produces hole pockets with a well defined Fermi surface. On further doping, $delta approx 10%sim 20%$ SDW order and coherent hole Fermi pockets are found at both strong and intermediate coupling. At even higher doping $delta gtrsim 20%$, the SDW order is suppressed and the spin-singlet Cooper pair correlations are simultaneously enhanced. We interpret this as the onset of superconductivity on suppressing magnetic order. We also briefly comment on the strong particle hole asymmetry of the model, and contrast electron versus hole doping.
The frustrated XY model on the honeycomb lattice has drawn lots of attentions because of the potential emergence of chiral spin liquid (CSL) with the increasing of frustrations or competing interactions. In this work, we study the extended spin-$frac
{1}{2}$ XY model with nearest-neighbor ($J_1$), and next-nearest-neighbor ($J_2$) interactions in the presence of a three-spins chiral ($J_{chi}$) term using density matrix renormalization group methods. We obtain a quantum phase diagram with both conventionally ordered and topologically ordered phases. In particular, the long-sought Kalmeyer-Laughlin CSL is shown to emerge under a small $J_{chi}$ perturbation due to the interplay of the magnetic frustration and chiral interactions. The CSL, which is a non-magnetic phase, is identified by the scalar chiral order, the finite spin gap on a torus, and the chiral entanglement spectrum described by chiral $SU(2)_{1}$ conformal field theory.
We report the existence of the charge density wave (CDW) in the ground state of 1D Kondo lattice model at the filling of n=0.75 in the weak coupling region. The CDW is driven by the effective Coulomb repulsion mediated by the localized spins. Based o
n our numerical results using the density matrix renormalization group method, we show that the CDW phase appears in the paramagnetic region previously known as the Tomonaga-Luttinger liquid. The emergence of this phase serves as an example of CDW phase induced without bare repulsive interactions, and enriches the phase diagram of the 1D Kondo lattice model.
We investigate the non-Abelian topological chiral spin liquid phase in the two-dimensional (2D) Kitaev honeycomb model subject to a magnetic field. By combining density matrix renormalization group (DMRG) and exact diagonalization (ED) we study the e
nergy spectra, entanglement, topological degeneracy, and expectation values of Wilson loop operators, allowing for robust characterization. While the ferromagnetic (FM) Kitaev spin liquid is already destroyed by a weak magnetic field with Zeeman energy $H_*^text{FM} approx 0.02$, the antiferromagnetic (AFM) spin liquid remains robust up to a magnetic field that is an order of magnitude larger, $H_*^text{AFM} approx 0.2$. Interestingly, for larger fields $H_*^text{AFM} < H < H_{**}^text{AFM}$, an intermediate gapless phase is observed, before a second transition to the high-field partially-polarized paramagnet. We attribute this rich phase diagram, and the remarkable stability of the chiral topological phase in the AFM Kitaev model, to the interplay of strong spin-orbit coupling and frustration enhanced by the magnetic field. Our findings suggest relevance to recent experiments on RuCl$_3$ under magnetic fields.
