arXiv subjects

D. N. Sheng

Publications and source records attributed to D. N. Sheng.

At least 37 records · Page 2Linked to original sources

arXiv2024

Magnetic field induced partially polarized chiral spin liquid in a transition metal dichalcogenide moiré system

As one of the most intriguing states of matter, the chiral spin liquid (CSL) has attracted much scientific interest while its existence and mechanism in crystalline strongly correlated systems remain hotly debated. On the other hand, strong correlation driven emergent phenomena can be realized in twisted transition metal dichalcogenide bilayers with a tremendously tunable large length scale providing a new platform for the emergence of CSLs. We focus on a strongly correlated model relevant to heterobilayer $\textrm{WSe}_{2}/\textrm{MoSe}_{2}$ and investigate the Mott insulating phase at half filling under an out-of-plane magnetic field. Considering both its orbital and spin Zeeman effects we identify three conventionally ordered phases including a $120^{\circ}$ Néel phase, a stripe phase, and an up-up-down phase. For intermediate fields an emergent quantum spin liquid phase is identified with partial spin polarization. We further characterize its topological nature as the $ν$ = 1/2 Laughlin CSL through the topological entanglement spectrum and quantized spin pumping under spin flux insertion. In addition, we map out the quantum phase diagram for different twisted angles in an experimentally accessible parameter regime.

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arXiv2024

Chiral spin liquid and quantum phase diagram of spin-$1/2$ $J_1$-$J_2$-$J_χ$ model on the square lattice

We study the spin-$1/2$ Heisenberg model on the square lattice with the first and second nearest-neighbor antiferromagnetic couplings $J_1$, $J_2$, as well as the three-spin scalar chiral coupling $J_χ$. Using density matrix renormalization group calculations, we obtain a quantum phase diagram of this system for $0 \leq J_2/J_1 \leq 1.0$ and $0 \leq J_χ/J_1 \leq 1.5$. We identify the Néel and stripe magnetic order phase at small $J_χ$ coupling. With growing $J_χ$, we identify the emergent chiral spin liquid (CSL) phase characterized by the quantized spin Chern number $C = 1/2$ and entanglement spectrum with the quasidegenerate group of levels agreeing with chiral SU(2)$_1$ conformal field theory, which is an analog of the $ν= 1/2$ Laughlin state in spin system. In the vicinity of the Néel and CSL phase boundary, our numerical results do not find evidence to support the phase coexistence of Néel order and topological order that was conjectured by mean-field calculations. In the larger $J_2$ and $J_χ$ coupling regime, the entanglement spectrum of the ground state also exhibits the chiral quasidegeneracy consistent with a CSL, but the adiabatic flux insertion simulations fail to obtain the quantized Chern number. By analyzing the finite-size scaling of magnetic order parameter, we find the vanished magnetic order suggesting a magnetic disorder phase, whose nature needs further studies. Different from the spin-$1$ $J_1$-$J_2$-$J_χ$ model, we do not find the coexistent stripe magnetic order and topological order. We also investigate the $J_χ$ dominant regime and find a strong tendency of the system to develop a dimer order rather than the chiral spin magnetic order observed in the spin-$1$ model.

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arXiv2024

Emergent Superconductivity and Competing Charge Orders in Hole-Doped Square-Lattice $t$-$J$ Model

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 (DMRG) simulations on the extended $t$-$J$ model have identified $d$-wave SC on the electron-doped side (with the next-nearest-neighbor hopping $t_2>0$) but a dominant charge density wave (CDW) order on the hole-doped side ($t_2<0$), 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 DMRG calculations with much enhanced bond dimensions, allowing more accurate determination of the ground state. On 6-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 8-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 $t$-$J$ models through weakening the competing charge orders, but also provide a unified understanding on the SC of both hole- and electron-doped cuprate superconductors.

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arXiv2024

Quantum Melting of Generalized Wigner Crystals in Transition Metal Dichalcogenide Moiré Systems

Generalized Wigner Crystal (GWC) is a novel quantum phase of matter driven by further-range interaction at fractional fillings of a lattice. The role of further range interaction as the driver for the incompressible state is akin to Wigner crystal. On the other hand, the significant role of commensurate filling is akin to the Mott insulator. Recent progress in simulator platforms presents unprecedented opportunities to investigate quantum melting in the strongly interacting regime through synergy between theory and experiments. However, the earlier theory literature presents diverging predictions. We study the quantum freezing of GWC through large-scale density matrix renormalization group simulations of a triangular lattice extended Hubbard model. We find a single first-order phase transition between the Fermi liquid and the $\sqrt{3}\times\sqrt{3}$ GWC state. The GWC state shows long-range antiferromagnetic $120^\circ$ N{é}el order. Our results present the simplest answers to the question of the quantum phase transition into the GWC phase and the properties of the GWC phase.

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arXiv2023

Singlet, Triplet and Pair Density Wave Superconductivity in the Doped Triangular-Lattice Moiré System

Recent experimental progress has established the twisted bilayer transition metal dichalcogenide (TMD) as a highly tunable platform for studying many-body physics. Particularly, the homobilayer TMDs under displacement field are believed to be described by a generalized triangular-lattice Hubbard model with a spin-dependent hopping phase $θ$. To explore the effects of $θ$ on the system, we perform density matrix renormalization group calculations for the relevant triangular lattice t-J model. By changing $θ$ at small hole doping, we obtain a region of quasi-long-range superconducting order coexisting with charge and spin density wave within $0<θ<π/3$. The superconductivity is composed of a dominant spin singlet $d$-wave and a subdominant triplet $p$-wave pairing. Intriguingly, the $S_z=\pm 1$ triplet pairing components feature pair density waves. In addition, we find a region of triplet superconductivity coexisting with charge density wave and ferromagnetism within $π/3<θ<2π/3$, which is related to the former phase at smaller $θ$ by a combined operation of spin-flip and gauge transformation. Our findings provide insights and directions for experimental search for exotic superconductivity in twisted TMD systems.

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arXiv2023

Anomalous Bilayer Quantum Hall Effect

In parallel to the condensed-matter realization of quantum Hall (Chern insulators), quantum spin Hall (topological insulators), and fractional quantum Hall (fractional Chern insulators) effects, we propose that bilayer flat band (FB) lattices with one FB in each layer constitute solid-state analogues of bilayer quantum Hall (BQH) system, leading to anomalous BQH (ABQH) effect, without magnetic field. By exact diagonalization of a bilayer Kagome lattice Hamiltonian, as a prototypical example, we demonstrate the stabilization of excitonic condensate Halperin's (1,1,1) state at the total filling $v_T=1$ of the two Fbs. Furthermore, by tuning the inter-layer tunneling and distance between the Kagome layers at $v_T=2/3$, we show phase transitions among Halperin's (3,3,0), spin-singlet (1,1,2), and particle-hole conjugate of Laughlin's 1/3 states, as previously observed in BQH systems. Our work opens a new research direction in the field of FB physics by demonstrating bilayer FB materials as an attractive avenue for realizing exotic ABQH states including non-Abelian anyons.

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arXiv2023

Quantum Phases of Transition Metal Dichalcogenide Moiré Systems

Moiré systems provide a rich platform for studies of strong correlation physics. Recent experiments on hetero-bilayer transition metal dichalcogenide (TMD) Moiré systems are exciting in that they manifest a relatively simple model system of an extended Hubbard model on a triangular lattice. Inspired by the prospect of the hetero-TMD Moiré system's 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.

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arXiv2023

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 work, 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 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.

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arXiv2023

Superconductivity in lightly doped Hubbard model on honeycomb lattice

We have performed large-scale density-matrix renormalization group studies of the lightly doped Hubbard model on the honeycomb lattice on long three and four-leg cylinders. We find that the ground state of the system upon lightly doping is consistent with that of a superconducting state with coexisting quasi-long-range superconducting and charge density wave orders. Both the superconducting and charge density wave correlations decay as a power law at long distances with corresponding exponents $K_{sc}<2$ and $K_c<2$. On the contrary, the spin-spin and single-particle correlations decay exponentially, although with relatively long correlation lengths.

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arXiv2023

Characterizing Random-singlet State in Two-dimensional Frustrated Quantum Magnets and Implications for the Double Perovskite Sr$_2$CuTe$_{1-x}$W$_{x}$O$_6$

Motivated by experimental observation of the non-magnetic phase in the compounds with frustration and disorder, we study the ground state of the spin-$1/2$ square-lattice Heisenberg model with randomly distributed nearest-neighbor $J_1$ and next-nearest-neighbor $J_2$ couplings. By using the density matrix renormalization group (DMRG) calculation on cylinder system with circumference up to $10$ lattice sites, we identify a disordered phase between the Néel and stripe magnetic phase with growing $J_2 / J_1$ in the presence of strong bond randomness. The vanished spin-freezing parameter indicates the absence of spin glass order. The large-scale DMRG results unveil the size-scaling behaviors of the spin-freezing parameter, the power-law decay of the average spin correlation, and the exponential decay of the typical spin correlation, which all agree with the corresponding behavior in the one-dimensional random singlet (RS) state and characterize the RS nature of this disordered phase. The DMRG simulation also provides insights and opportunities for characterizing a class of non-magnetic states in two-dimensional frustrated magnets with disorder. We also compare with existing experiments and suggest more measurements for understanding the spin-liquid-like behaviors in the double perovskite Sr$_2$CuTe$_{1-x}$W$_{x}$O$_6$.

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arXiv2022

Global quantum phase diagram and non-Abelian chiral spin liquid in a spin-3/2 square lattice antiferromagnet

Since strong quantum fluctuations are essential for the emergence of quantum spin liquids, there have been extensive exploration and identification of spin liquid candidates in spin-$1/2$ systems, while such activities are rare in higher spin systems. Here we report an example of non-Abelian chiral spin liquid emerging in spin-$3/2$ Heisenberg model on a square lattice. By tuning Heisenberg exchange interaction and scalar chirality interaction, we map out a quantum phase diagram enclosing three conventional magnetic orders and a chiral spin liquid based on density matrix renormalization group studies. The nature of the spin liquid is identified as a long-sought bosonic version of Read-Rezayi state that supports non-Abelian Fibonacci anyonic statistics, identified by the ground state entanglement spectrum. Significantly, we establish that the non-Abelian CSL emerges through the enlarged local degrees of freedom and enhanced quantum fluctuations near the classical phase boundaries of competing magnetic orders. Our numerical discovery of an exotic quantum spin liquid in spin-$3/2$ system suggests a new route for discovering fractionalized quantum phases in frustrated higher spin magnetic compounds.

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arXiv2022

Interaction-driven quantum anomalous Hall insulator in Dirac semimetal

The interaction-driven quantum anomalous Hall (QAH) insulator has been sought for a long time in a Dirac semimetal with linear band touching points at the Fermi level. By combining exact diagonalization, density matrix renormalization group, and analytical methods, we study a spinless fermion system on the checkerboard lattice with two fold rotational symmetry, which realizes two Dirac band touching points in the absence of interaction. At weak coupling, the Dirac semimetal is stable. At a finite density-density repulsive interaction, we analyze possible symmetry broken states, and find that an QAH state is stabilized when the interaction strength exceeds the energy scale controlling the separation between the Dirac points. Through numerical simulations, we verify the existence of the QAH phase with spontaneous time-reversal symmetry breaking and quantized Chern number $C = 1$.

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arXiv2022

Quantum Spin Liquid with Emergent Chiral Order in the Triangular-lattice Hubbard Model

The interplay between spin frustration and charge fluctuation gives rise to an exotic quantum state in the intermediate-interaction regime of the half-filled triangular-lattice Hubbard model, while the nature of the state is under debate. Using the density matrix renormalization group with SU(2)$_{\rm{spin}} \otimes $U(1)$_{\rm{charge}}$ symmetries implemented, we study the triangular-lattice Hubbard model defined on the long cylinder geometry up to circumference $W=6$. A gapped quantum spin liquid, with on-site interaction $9 \lesssim U / t \lesssim 10.75$, is identified between the metallic and the antiferromagnetic Mott insulating phases. In particular, we find that this spin liquid develops a robust long-range spin scalar-chiral correlation as the system length $L$ increases, which unambiguously unveils the spontaneous time-reversal symmetry breaking. In addition, the degeneracy of the entanglement spectrum supports symmetry fractionalization and spinon edge modes in the obtained ground state. The possible origin of chiral order in this intermediate spin liquid and its relation to the rotonlike excitations have also been discussed.

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arXiv2022

Topological flat bands in a kagomé lattice multiorbital system

Flat bands and dispersive Dirac bands are known to coexist in the electronic bands in a two-dimensional kagome lattice. Including the relativistic spin-orbit coupling, such systems often exhibit nontrivial band topology, allowing for gapless edge modes between flat bands at several locations in the band structure, and dispersive bands or at the Dirac band crossing. Here, we theoretically demonstrate that a multiorbital system on a kagome lattice is a versatile platform to explore the interplay between nontrivial band topology and electronic interaction. Specifically, here we report that the multiorbital kagome model with the atomic spin-orbit coupling naturally supports topological bands characterized by nonzero Chern numbers $\cal C$, including a flat band with $|{\cal C}| =1$. When such a flat band is $1/3$ filled, the non-local repulsive interactions induce a fractional Chern insulating state. We also discuss the possible realization of our findings in real kagome materials.

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arXiv2022

Topological chiral and nematic superconductivity by doping Mott insulators on triangular lattice

The mechanism of the unconventional topological superconductivity (TSC) remains a long-standing issue. We investigate the quantum phase diagram of the extended $t$-$J$-$J_χ$ model including spin chiral interactions on triangular lattice based on the state-of-the-art density matrix renormalization group simulations. We identify distinct classes of superconducting phases characterized by nonzero topological Chern numbers $C=1$ and $2$, and a nematic d-wave superconducting phase with a zero Chern number. The TSC states are shown to emerge from doping either a magnetic insulator or chiral spin liquid, which opens new opportunities for experimental discovery. In addition, we further classify the $C=2$ class of TSC phases into an isotropic and a nematic TSC phases, and present evidence of continuous quantum phase transitions from the nematic TSC phase to both isotropic TSC and nematic d-wave phases. These results provide new insight into the mechanism of TSC with an emphasis on the role played by hole dynamics, which changes spin background and drives a topological phase transition at a hole doping level around $3\%$ upon doping a magnetic insulator to enable the emergence of the TSC.

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arXiv2022

Coexistence of non-Abelian chiral spin liquid and magnetic order in a spin-1 antiferromagnet

We study the ground-state properties of a spin-1 Heisenberg model on a square lattice with the first- and second-nearest-neighbor antiferromagnetic couplings $J_1$ and $J_2$ and a three-spin scalar chirality term $J_χ$. Using the density matrix renormalization group calculation, we map out a global phase diagram including various magnetic order phases and an emergent quantum spin liquid phase. The nature of the spin liquid is identified as a bosonic non-Abelian Moore-Read state from the fingerprint of the entanglement spectra and identification of a full set of topological sectors. We further unveil a stripe magnetic order coexisting with this spin liquid. Our results not only establish a rare example of non-Abelian spin liquids in simple spin systems but also demonstrate the coexistence of fractionalized excitations and magnetic order beyond mean-field descriptions.

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arXiv2022

Doped Mott Insulators in the Triangular Lattice Hubbard Model

We investigate the evolution of the Mott insulators in the triangular lattice Hubbard Model, as a function of hole doping $δ$ in both the strong and intermediate coupling limits. Using the advanced density matrix renormalization group (DMRG) method, at light hole doping $δ\lesssim 10\%$, 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, this chiral metal also exhibits staggered loop current, which breaks the translational symmetry. 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, $δ\approx 10\%\sim 20\%$ SDW order and coherent hole Fermi pockets are found at both strong and intermediate couplings. At even higher doping $δ\gtrsim 20\%$, the SDW order is suppressed and the spin-singlet Cooper pair correlations are simultaneously enhanced. We also briefly comment on the strong particle-hole asymmetry of the model.

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arXiv2021

SU(4) chiral spin liquid, exciton supersolid and electric detection in moiré bilayers

We propose moiré bilayer as a platform where exotic quantum phases can be stabilized and electrically detected. Moiré bilayer consists of two separate moiré superlattice layers coupled through the inter-layer Coulomb repulsion. In the small distance limit, an SU(4) spin can be formed by combining layer pseudospin and the real spin. As a concrete example, we study an SU(4) spin model on triangular lattice in the fundamental representation. By tuning a three-site ring exchange term $K\sim \frac{t^3}{U^2}$, we find SU(4) symmetric crystallized phase and an SU(4)$_1$ chiral spin liquid (CSL) at the balanced filling. We also predict two different exciton supersolid phases with inter-layer coherence at imbalanced filling under displacement field. Especially, the system can simulate an SU(2) Bose-Einstein-condensation (BEC) by injecting inter-layer excitons into the magnetically ordered Mott insulator at the layer polarized limit. Smoking gun evidences of these phases can be obtained by measuring the pseudo-spin transport in the counter-flow channel.

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