arXiv subjects

Shou-Shu Gong

Publications and source records attributed to Shou-Shu Gong.

At least 19 recordsLinked to original sources

arXiv2026

Non-Abelian chiral spin liquid in a spin-$1$ antiferromagnet on the square lattice

Non-Abelian chiral spin liquids (CSLs) host non-Abelian anyon excitations and are promising platforms for topological quantum computation. However, realizing non-Abelian CSLs in short-range interacting spin systems remains elusive. Here, we study a spin-$1$ square-lattice model with the first- and second-neighbor bilinear ($J_1,J_2$) and biquadratic interactions ($K_1,K_2$), as well as the three-spin scalar chiral coupling $J_χ$. Inspired by the evidence of the Moore-Read state in exact diagonalization and infinite Projected Entangled Pair States calculations, we fix $J_1=1.0$, $J_2/J_1=0.623$, $K_1/J_1=-0.176$, and obtain a quantum phase diagram for $0 \leq K_2/J_1 \leq 0.4$ and $0.3 \leq J_χ/J_1 \leq 0.6$ by using the density matrix renormalization group (DMRG) calculations. We identify a stripe antiferromagnetic phase, a Néel antiferromagnetic phase, a magnetically ordered chiral spin state phase, and a non-Abelian CSL phase emerging near the boundaries of the ordered phases. The unbiased DMRG results provide strong evidence for the Moore-Read state, including the three topological sectors, the quantized spin Chern number $C=1$, and the level counting of low-lying entanglement spectra which is consistent with the chiral SU(2)$_2$ conformal field theory. Our results may shed new light on searching for non-Abelian CSLs in other higher-spin ($S > 1/2$) systems with short-range couplings.

cond-mat.str-el↗

arXiv2026

Distinct many-body scars and emergent quantum phases driven by competing interactions in two-species Rydberg arrays

Rydberg atom arrays composed of multiple atomic species stand as a highly promising platform for quantum computation. However, the underlying physics of these systems as quantum many-body systems remains poorly understood, owing to the intricate competition between attractive and repulsive interactions, phenomena that entirely defy the Rydberg blockade mechanism. We systematically calculate the ground-state phase diagram of alternating two-species atom arrays and their quench dynamics. Our findings reveal several novel quantum states absent in traditional cold-atom platforms, such as the period-4 product state $|1100...\rangle$, the period-6 product state $|111000...\rangle$, and an order-disorder mixed phase. In the quench dynamics, we confirm $\mathbb{Z}_2$ ordered state qualify as novel quantum many-body scars. Based on our perturbation analysis, the underlying physics ought to be described by a series of Cooper pair states spanning the entire energy spectrum, rather than the PXP low-energy effective model. A detailed analysis is also provided regarding the experimental preparation of those product states. Numerical evidence demonstrates that the proposed scheme exhibits robustness against typical experimental imperfections, thereby confirming its experimental feasibility. Moreover, the ground-state problem of the two-species array naturally maps to more general combinatorial optimization problems, extending the class of optimization tasks accessible to programmable neutral-atom quantum processors. Our work paves a new way for quantum simulation of novel quantum many-body states, which emerge from the interplay between competing interactions among different atom species and quantum fluctuations.

cond-mat.quant-gas↗

arXiv2026

Spiral and Mixed Plaquette-Dimer Phases in the $S=1$ and $3/2$ Shastry-Sutherland Heisenberg Model

We investigate the ground-state phase diagram of the $S=1$ and $S=3/2$ Heisenberg model on the two-dimensional Shastry-Sutherland lattice (SSL) using density matrix renormalization group (DMRG) and cluster mean-field theory (CMFT). Between the dimer phase and Néel antiferromagnetic phases, we identify two intermediate phases: a mixed plaquette-dimer (MPD) phase and a spiral phase. These phases are characterized via bond energies and spin-spin correlation functions; phase boundaries are located from the ground-state energy derivative and entanglement entropy. The MPD phase exhibits strong intradimer correlations and weak tetramerization on the empty plaquettes, and its transitions to the dimer and spiral phases are first order. Combining our results with the known boundaries for $S=1/2$ and the classical limit $S\to\infty$, we construct a global $S$-$g$ phase diagram. This diagram reveals the progressive suppression of quantum effects with increasing $S$ and offers a theoretical framework for larger-$S$ SSL materials.

cond-mat.str-el↗

arXiv2026

Competing and Intertwined Orders in Boson-Doped Mott Antiferromagnets

Inspired by the recent experimental advances in cold atom quantum simulators, we explore the experimentally implemented bosonic $t$-$t'$-$J$ model on the square lattice using large-scale density matrix renormalization group simulations. By tuning the doping level $δ$ and hopping ratio $t'/t$, we uncover six distinct quantum phases, several of which go far beyond the conventional paradigm of phase-coherent superfluidity (SF) expected for bosonic systems. In particular, in the presence of antiferromagnetic (AFM) order, doped holes are tightly bound into pairs, giving rise to a pair density wave (PDW) phase at low doping and small $|t'/t|$, which is suppressed on the $t'<0$ side, resulting in a disordered PDW state that lacks coherence of either individual bosons or pairs. Upon further doping, bosons can regain phase coherence and form a SF* state, characterized by condensation at emergent incommensurate momenta concurrent with an incommensurate magnetic order. On the $t'>0$ side, the sign-induced kinetic frustration inherently disfavors local AFM correlations, leading to a phase separation in which doped holes cluster into ferromagnetic (FM) domains spatially separated by undoped AFM regions. Upon further doping, this inhomogeneous state evolves into a uniform SF + $xy$-FM phase. Finally, we propose a concrete experimental scheme to realize both signs of $t'/t$ in Rydberg tweezer arrays, with an explicit mapping between model parameters and experimentally accessible regimes. Our results reveal competing and intertwined orders in doped antiferromagnets, which are relevant to central issues in high-$T_c$ superconductivity, reflecting the frustrated interplay between doped holes and spin background.

cond-mat.str-el↗

arXiv2025

Fermi-liquid-like phase driven by next-nearest-neighbor couplings in a lightly doped kagome-lattice $t$-$J$ model

Due to the interplay between charge fluctuation and geometry frustration, the doped kagome-lattice Mott insulator is a fascinating platform to realize exotic quantum states. Through the state-of-the-art density matrix renormalization group calculation, we explore the quantum phases of the lightly doped kagome-lattice $t$-$J$ model in the presence of the next-nearest-neighbor electron hopping $t_2$ and spin interaction $J_2$. On the $L_y = 3$ cylinder ($L_y$ is the number of unit cells along the circumference direction), we establish a quantum phase diagram with tuning $t_2 > 0$ and $J_2 > 0$, showing an emergent Fermi-liquid-like phase driven by increased $t_2$ and $J_2$, which sits at the neighbor of the previously identified charge density wave (CDW) phase. Compared with the CDW phase, the charge order is significantly suppressed in the Fermi-liquid-like phase, and most correlation functions are greatly enhanced with power-law decay. In particular, we find the absence of hole pairing and a strong three-sublattice magnetic correlation. On the wider $L_y = 4$ cylinder, this Fermi-liquid-like phase persists at low doping levels, strongly suggesting that this state might be stable in the two-dimensional kagome system.

cond-mat.str-el↗

arXiv2025

Emergent Fermi-liquid-like phase by melting a holon Wigner crystal in a doped Mott insulator on the kagome lattice

The doped quantum spin liquid on the kagome lattice provides a fascinating platform to explore exotic quantum states, such as the reported holon Wigner crystal at low doping. By extending the doping range to $δ= 0.027$ - $0.36$, we study the kagome-lattice $t$-$J$ model using the state-of-the-art density matrix renormalization group calculation. On the $L_y=3$ cylinder ($L_y$ is the number of unit cells along the circumference direction), we establish a quantum phase diagram with increasing doping level. In addition to the charge density wave (CDW) states at lower doping, we find an emergent Fermi-liquid-like phase by melting the holon Wigner crystal at $δ\approx 0.15$, which is characterized by suppression of charge density oscillation and power-law decay of various correlation functions. On the wider $L_y = 4$ cylinder, the bond-dimension extrapolated correlation functions also support such a Fermi-liquid-like state, suggesting its stability with increasing system size. In a narrow doping range near $δ= 1/3$ on the $L_y = 3$ cylinder, we find a state with an exponential decay of single-particle correlation but the other correlation functions preserving the features in the Fermi-liquid-like phase, which may be a precursor of a superconducting state. Nevertheless, this peculiar state near $δ= 1/3$ disappears on the $L_y = 4$ cylinder, implying a possible lattice size dependence. Our results reveal a quantum melting from a holon Wigner crystal to a Fermi-liquid-like state with increasing hole density, and suggest a doping regime to explore superconductivity for future study.

cond-mat.str-el↗

arXiv2025

Superconductivity of bilayer two-orbital Hubbard model for La$_{3}$Ni$_{2}$O$_{7}$ under high pressure

By combining density functional theory (DFT) and density matrix renormalization group calculations, we investigate the unusual pressure dependence of superconducting transition temperature ($T_c$) in the nickelate superconductor La$_{3}$Ni$_{2}$O$_{7}$. Using the hopping integrals and on-site potentials obtained by fitting the DFT band structures, we map a quantum phase diagram of a bilayer two-orbital Hubbard model with increasing pressure in a ladder geometry, which has an intermediate Hubbard repulsion and a Hund's coupling. Near $3/8$ filling, we find a strong spin density wave order, which at $3/8$ filling shows a real-space spin pattern similar to the spin-charge stripe order along a lattice direction. At $21/64$ filling, we find a superconducting phase with interlayer superconductivity (SC) in both the $d_{z^2}$ and $d_{x^2-y^2}$ orbitals, as well as in-plane SC in the $d_{z^2}$ orbital. Intriguingly, the SC is weakened with increasing pressure and transits to a Luttinger liquid above $80$ GPa, which qualitatively agrees with the experimental observations of decreasing $T_c$ with increasing pressure and a transition to Fermi liquid above $80$ GPa in La$_{3}$Ni$_{2}$O$_{7}$. Through a comparative study, we further show that the ratio of interaction to hopping integral, which reduces moderately with increasing pressure, may play a dominant role in the weakening of SC. Our results of this experimentally relevant model not only find a robust SC through suppressing the competing spin density wave order, but also give new insight into the unusual pressure dependence of SC in La$_{3}$Ni$_{2}$O$_{7}$.

cond-mat.supr-con↗

arXiv2025

Evolution from intralayer to interlayer superconductivity in a bilayer $t$-$J$ model

Motivated by the bilayer cuprate superconductors and nickelate superconductor La$_3$Ni$_2$O$_7$, we investigate the evolution from intralayer to interlayer superconductivity based on a bilayer two-leg $t$-$J$-$J_{\bot}$ model, where $t$ is the in-plane electron hopping, $J$ is the in-plane spin interaction, and $J_{\bot}$ is the inter-plane spin interaction. By means of the density matrix renormalization group calculations, we obtain the quantum phase diagram of the system by tuning $J_{\bot}$ in a large doping range $δ= 1/8 - 1/2$. We find that a large $J_{\bot}$ can always drive an interlayer superconductivity by coupling the two layers in both the Luther-Emery liquid and Luttinger liquid states. By coupling two Luther-Emery liquid states, the in-plane superconductivity evolves to inter-plane superconductivity either through an intermediate charge density wave (CDW) phase or directly, depending on doping ratio. This emergent CDW phase, which exists over a finite doping range, appears to develop from the CDW state of the two-leg ladder at $δ= 1/4$. By coupling two Luttinger liquids, the in-plane Luttinger liquids show a transition to the inter-plane superconducting phase at large $J_{\bot}$, as reported in previous literature. Interestingly, in the intermediate $J_{\bot}$ regime we find that while the in-plane Luttinger-liquid features remain stable, the inter-plane superconductivity can develop an enhanced quasi-long-range order with the power exponent $K^{zz}_{\rm SC} \sim 1$. At last, we show that the interlayer superconductivity is also stable by coupling the bilayer three-leg $t$-$J$ ladders by a strong $J_{\bot}$ interaction, from both the Luther-Emery liquid and Luttinger-liquid states.

cond-mat.str-el↗

arXiv2025

Tuning competition between charge order and superconductivity in the square-lattice $t$-$t'$-$J$ model

Recently, a flurry of works have found strong competition between charge density wave (CDW) and superconductivity (SC) in the doped Hubbard and $t$-$J$ models on the square lattice. Interestingly, some recent results suggest that the electron-phonon coupling may suppress CDW order and enhance SC. In this work, we consider the square-lattice Hubbard model with the Holstein or Su-Schrieffer-Heeger electron-phonon coupling at the large-$U$ and antiadiabatic (infinite phonon frequency) limit, which gives an effective $t$-$J$ model with either a density attractive interaction $V$ or a $J_P$ term that contributes a larger spin exchange and a density repulsive interaction. To explore how these effective couplings may suppress CDW and give a SC, we implement the density matrix renormalization group simulation on the $t$-$t'$-$J$ model with $V$ or $J_P$ coupling. We focus on the {\it six-leg} cylinder system with the next-nearest-neighbor hopping $t'$, which hosts partially filled stripe and $d$-wave SC in phase diagram. By tuning $t'/t > 0$ and $V$ or $J_P$, we establish two quantum phase diagrams. In the SC phases, the increased $V$ or $J_P$ coupling can enhance the quasi-long-range SC order, consistent with some previous findings. Nonetheless, no SC emerges when the partially filled stripe phase disappears with increased $V$ or $J_P$. Instead, the system has a transition to either a phase-separation-like regime or a filled stripe phase. On the other hand, with increased $t'/t$, not only the partially filled stripe but the phase separation and filled stripe can also be tuned to SC phase. Our results suggest that although $V$ and $J_P$ couplings may strengthen hole binding, the hole dynamics controlled by $t'/t$ appears to play more crucial role for obtaining a SC in $t$-$J$ model.

cond-mat.str-el↗

arXiv2024

Phase Diagram, $d$-Wave Superconductivity, and Pseudogap of the $t$-$t'$-$J$ Model at Finite Temperature

Recently, robust $d$-wave superconductive (SC) order has been unveiled in the ground state of the 2D $t$-$t'$-$J$ model -- with both nearest-neighbor ($t$) and next-nearest-neighbor ($t'$) hoppings -- by density matrix renormalization group studies. However, there is currently a debate on whether the $d$-wave SC holds up strong on both $t'/t>0$ and $t'/t<0$ cases for the $t$-$t'$-$J$ model, which correspond to the electron- and hole-doped sides of the cuprate phase diagram, respectively. Here we exploit state-of-the-art thermal tensor network approach to accurately obtain the phase diagram of the $t$-$t'$-$J$ model on cylinders with widths up to $W=6$ and down to low temperature as $T/J \simeq 0.06$, pushing the boundaries of contemporary finite-$T$ calculations. For $t'/t>0$, we find a dome-like SC regime with a diverging $d$-wave pairing susceptibility, $χ_\textrm{SC} \propto 1/T^α$ below a characteristic temperature $T_c^*$. Near optimal doping, $T_c^*$ reaches its highest value of about $0.15 J$. Above $T_c^*$ yet below a higher crossover temperature $T^*$, the magnetic susceptibility becomes suppressed, which can be related to the onset of pseudogap (PG) behaviors. On the other hand, for $t'/t<0$ we find the pairing correlations are much weaker, although there exhibits a node-antinode structure in the PG regime as observed in the hole-doped cuprates. The thermal tensor network calculations of the $t$-$t'$-$J$ model underscore both the similarities and differences in the finite-temperature phase diagram between the fundamental model and cuprates, yielding unique insights into their intricate behaviors.

cond-mat.str-el↗

arXiv2024

Sign structure of the $t$-$t^\prime$-$J$ model and its physical consequences

Understanding the doped Mott insulator is a central challenge in condensed matter physics. In this work, we first explicitly identify a new sign structure in the $t$-$t'$-$J$ model on the square lattice that replaces the conventional Fermi statistics for weakly interacting electrons. Then we show that the singular, i.e., the phase-string part of the sign structure in the partition function can be precisely turned off in a modified model. The density matrix renormalization group method is then employed to study these two models comparatively on finite-size systems, which is designed to unveil the consequences of the phase-string component. We find that the hole pairing is present not only in the quasi-long-range superconducting phase but also in the stripe phase of the $t$-$t'$-$J$ model. However, once the phase-string is switched off, both the superconducting and stripe orders together with the underlying hole pairing disappear. The corresponding ground state reduces to a trivial Fermi-liquid-like state with small hole Fermi pockets that is decoupled from the antiferromagnetic spin background. It is in sharp contrast to the original $t$-$t'$-$J$ model where large Fermi surfaces can be restored in the stripe phase found at $t'/t<0$ or the superconducting phase at $t'/t>0$ in the six-leg ladder calculation. Our study clearly demonstrates that the strong correlation effect in doped Mott insulator should be mainly attributed to the long-range quantum entanglement between the spin and charge, which is, non-perturbatively, beyond a simple spin-charge separation under the no double occupancy constraint.

cond-mat.str-el↗

arXiv2024

Quantum criticality with emergent symmetry in the extended Shastry-Sutherland model

Motivated by the novel phenomena observed in the layered material $\rm SrCu_2(BO_3)_2$, the Shastry-Sutherland model (SSM) has been extensively studied as the minimal model for $\rm SrCu_2(BO_3)_2$. However, the nature of its quantum phase transition from the plaquette valence-bond solid (PVBS) to antiferromagnetic (AFM) phase is under fierce debate, posing a challenge to understand the underlying quantum criticality. Via the state-of-the-art tensor network simulations, we study the ground state of the SSM on large-scale size up to $20 \times 20$ sites. We identify the continuous transition nature accompanied by an emergent O(4) symmetry between the PVBS and AFM phase, which strongly suggests a deconfined quantum critical point (DQCP). Furthermore, we map out the phase diagram of an extended SSM that can be continuously tuned to the SSM, which demonstrates the same DQCP phenomena along a whole critical line. Our results indicate a compelling scenario for understanding the origin of the proposed proximate DQCP in recent experiments of $\rm SrCu_2(BO_3)_2$.

cond-mat.str-el↗

arXiv2024

Tensor network study of the spin-1/2 square-lattice $J_1$-$J_2$-$J_3$ model: incommensurate spiral order, mixed valence-bond solids, and multicritical points

We use the finite projected entangled pair state (PEPS) method to investigate the global phase diagram of the spin-1/2 square-lattice $J_1$-$J_2$-$J_3$ antiferromagnetic (AFM) Heisenberg model. The ground state phase diagram is established with a rich variety of phases: AFM, gapless quantum spin liquid, valence-bond solid (VBS), stripe, and incommensurate spiral phases. The nature of the VBS region is revealed, containing a plaquette VBS and a mixed columnar-plaquette VBS, with the emergence of short-range incommensurate spin correlations in some region. The long-range incommensurate magnetic phase is also explicitly characterized as a planar spiral with incommensurate spatial periodicities. Most interestingly, there exists several multicritical points connecting different phases. These findings elucidate the true nature of the long-standing square-lattice $J_1$-$J_2$-$J_3$ antiferromagnet at zero-temperature. Our results also pave the way to accurately simulate complex two-dimensional quantum systems that may host nonuniform features by means of finite PEPS.

cond-mat.str-el↗

arXiv2024

Exact Demonstration of pair-density-wave superconductivity in the $σ_z$-Hubbard model

Describing and achieving `unconventional' superconductivity remains a forefront challenge in quantum many-body physics. Here we use a unitary mapping, combined with the well-established properties of the attractive Hubbard model to demonstrate rigorously a Hamiltonian with a low temperature pair-density-wave (PDW) phase. We also show that the same mapping, when applied to the widely accepted properties of the repulsive Hubbard model, leads to a Hamiltonian exhibiting triplet $d$-wave PDW superconductivity and an unusual combination of ferro- and antiferro-magnetic spin correlations. We then demonstrate the persistence of the $d$-wave PDW in a Hamiltonian derived from the mapping of the extended $t$-$J$ model in the large-$U$ limit. Furthermore, through strategic manipulation of the nearest-neighbor hopping signs of spin-down electrons, we illustrate the attainability of PDW superconductivity at other momenta. The intertwining of different magnetic and exotic pairing correlations noted here may have connections to experimental observations in spin-triplet candidates like UTe$_2$.

cond-mat.supr-con↗

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.

cond-mat.str-el↗

arXiv2024

Field induced non-BEC transitions in frustrated magnets

Frustrated spin-systems have traditionally proven challenging to understand, owing to a scarcity of controlled methods for their analyses. By contrast, under strong magnetic fields, certain aspects of spin systems admit simpler and universal description in terms of hardcore bosons. The bosonic formalism is anchored by the phenomenon of Bose-Einstein condensation (BEC), which has helped explain the behaviors of a wide range of magnetic compounds under applied magnetic fields. Here, we focus on the interplay between frustration and externally applied magnetic field to identify instances where the BEC paradigm is no longer applicable. As a representative example, we consider the antiferromagnetic $J_1 - J_2 - J_3$ model on the square lattice in the presence of a uniform external magnetic field, and demonstrate that the frustration-driven suppression of the Néel order leads to a Lifshitz transition for the hardcore bosons. In the vicinity of the Lifshitz point, the physics becomes unmoored from the BEC paradigm, and the behavior of the system, both at and below the saturation field, is controlled by a Lifshitz multicritical point. We obtain the resultant universal scaling behaviors, and provide strong evidence for the existence of a frustration and magnetic-field driven correlated bosonic liquid state along the entire phase boundary separating the Néel phase from other magnetically ordered states.

cond-mat.str-el↗

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.

cond-mat.str-el↗

arXiv2023

Emergent Symmetry in Quantum Phase Transitions: From Deconfined Quantum Critical Point to Gapless Quantum Spin Liquid

The emergence of exotic quantum phenomena in frustrated magnets is rapidly driving the development of quantum many-body physics, raising fundamental questions on the nature of quantum phase transitions. Here we unveil the behaviour of emergent symmetry involving two extraordinarily representative phenomena, i.e., the deconfined quantum critical point (DQCP) and the quantum spin liquid (QSL) state. Via large-scale tensor network simulations, we study a spatially anisotropic spin-1/2 square-lattice frustrated antiferromagnetic (AFM) model, namely the $J_{1x}$-$J_{1y}$-$J_2$ model, which contains anisotropic nearest-neighbor couplings $J_{1x}$, $J_{1y}$ and the next nearest neighbor coupling $J_2$. For small $J_{1y}/J_{1x}$, by tuning $J_2$, a direct continuous transition between the AFM and valence bond solid phase is observed.(Of course, the possibility of weakly first order transition can not be fully excluded.) With growing $J_{1y}/J_{1x}$, a gapless QSL phase gradually emerges between the AFM and VBS phases. We observe an emergent O(4) symmetry along the AFM--VBS transition line, which is consistent with the prediction of DQCP theory. Most surprisingly, we find that such an emergent O(4) symmetry holds for the whole QSL--VBS transition line as well. These findings reveal the intrinsic relationship between the QSL and DQCP from categorical symmetry point of view, and strongly constrain the quantum field theory description of the QSL phase. The phase diagram and critical exponents presented in this paper are of direct relevance to future experiments on frustrated magnets and cold atom systems.

cond-mat.str-el↗