The criticality between the nematic and valence-bond-solid (VBS) phases was investigated for the two-dimensional quantum S=1-spin model with the three-spin and biquadratic interactions by means of the numerical diagonalization method. It is expected that the criticality belongs to a novel universality class, the so-called deconfined criticality, accompanied with unconventional critical indices. In this paper, we incorporate the three-spin interaction, and adjust the (redundant) interaction parameter so as to optimize the finite-size behavior. Treating the finite-size cluster with N \le 20 spins, we estimate the correlation-length critical exponent as ν=0.88 (3).
We study theoretically the destruction of spin nematic order due to quantum fluctuations in quasi-one dimensional spin-1 magnets. If the nematic ordering is disordered by condensing disclinations then quantum Berry phase effects induce dimerization in the resulting paramagnet. We develop a theory for a Landau-forbidden second order transition between the spin nematic and dimerized states found in recent numerical calculations. Numerical tests of the theory are suggested.
Deconfined quantum criticality with emergent SO(5) symmetry in correlated systems remains elusive. Here, by performing numerically-exact state-of-the-art quantum Monte Carlo (QMC) simulations, we show convincing evidences of deconfined quantum critical points (DQCP) between antiferromagnetic and valence-bond-solid phases in the extended Hubbard model of fermions on the honeycomb lattice with large system sizes. We further demonstrate evidences of the SO(5) symmetry at the DQCP. It is important to note that the critical exponents obtained by finite-size scaling at the DQCP here are consistent w…
Monte Carlo simulations of the SU(2)-symmetric deconfined critical point action reveal strong violations of scale invariance for the deconfinement transition. We find compelling evidence that the generic runaway renormalization flow of the gauge coupling is to a weak first order transition, similar to the case of U(1)$\times$U(1) symmetry. Our results imply that recent numeric studies of the Nèel antiferromagnet to valence bond solid quantum phase transition in SU(2)-symmetric models were not accurate enough in determining the nature of the transition.
Deconfined criticality as intrinsically gapless topological state in one dimension
Institute for Advanced Study in Physics and School of Physics, Zhejiang University（浙江大学物理学院和高等研究院）；Department of Physics, Nanjing University（南京大学物理系）；University of Colorado, Boulder（科罗拉多大学博尔德分校）；Harvard University（哈佛大学）；Department of Physics, University of California, San Diego（加州大学圣地亚哥分校物理系）；Fuzhou University（福州大学）；College of Physics and Information Engineering, Fuzhou University（福州大学物理与信息工程学院）
Duality places an important constraint on the renormalization group flows and the phase diagrams. For self-dual theories, the self-duality can be promoted as a symmetry, this leads to the multi-criticalities. This work investigates a description of the deconfined quantum criticality, the $N_f=2$ QED$_3$, as an example of self-dual theories and its multi-critical behavior under perturbative deformations. The multi-criticality is described by the theory with Gross-Neveu couplings and falls in a different universality class than the standard deconfined quantum criticality. We systematically calcu…
We continue recent efforts to discover examples of deconfined quantum criticality in one-dimensional models. In this work we investigate the transition between a $\mathbb{Z}_3$ ferromagnet and a phase with valence bond solid (VBS) order in a spin chain with $\mathbb{Z}_3\times\mathbb{Z}_3$ global symmetry. We study a model with alternating projective representations on the sites of the two sublattices, allowing the Hamiltonian to connect to an exactly solvable point having VBS order with the character of SU(3)-invariant singlets. Such a model does not admit a Lieb-Schultz-Mattis theorem typica…
The quantum S=1 spin model on the spatially anisotropic triangular lattice is investigated numerically. The nematic and valence-bond-solid (VBS) phases are realized by adjusting the spatial anisotropy and the biquadratic interaction. The phase transition between the nematic and VBS phases is expected to be a continuous one with unconventional critical indices (deconfined criticality). The geometrical character (spatial anisotropy) is taken into account by imposing the screw-boundary condition (Novotny's method). Diagonalizing the finite-size cluster with N \le 20 spins, we observe a clear indi…
Monte Carlo study of the deconfined critical action phase diagram reveals a region where spinon deconfinement occurs through a weak first-order phase transition, in agreement with Ginzburg-Landau theory. Wilson renormalization argument in combination with the absence of the data collapse even in the regime of weak interaction between the spinons casts a serious doubt on the possibility of the continuous deconfinement transition. We also argue that if a continuous deconfined criticality does exist on the phase diagram, its nature is analogous, in a certain precise sense, to that of the XY unive…
Quantum transition points in the J -Q model---the test bed of the deconfined critical point theory---and the SU(2)-symmetric discrete noncompact CP^1 representation of the deconfined critical action are directly compared by the flowgram method. We find that the flows of two systems coincide in a broad region of linear system sizes (10 < L < 50 for the J -Q model), implying that the deconfined critical point theory correctly captures the mesoscopic physics of competition between the antiferromagnetic and valence-bond orders in quantum spin systems. At larger sizes, however, we observe significa…
We perform a comparative Monte Carlo study of the easy-plane deconfined critical point (DCP) action and its short-range counterpart to reveal close similarities between the two models for intermediate and strong coupling regimes. For weak coupling, the structure of the phase diagram depends on the interaction range: while the short-range model features a tricritical point and a continuous U(1)xU(1) transition,the long-range DCP action is characterized by the runaway renormalization flow of coupling into a first (I) order phase transition. We develop a "numerical flowgram" method for high preci…
The J_1-J_2 model with the biquadratic (plaquette-four-spin) interaction was simulated with the numerical-diagonalization method. Some limiting cases of this model have been investigated thoroughly. Taking the advantage of the extended parameter space, we survey the phase boundary separating the N'eel and valence-bond-solid phases. According to the deconfined-criticality scenario, the singularity of this phase boundary is continuous, accompanied with unconventional critical indices. Diagonalizing the finite-size cluster with N \le 36 spins, we observe a signature of continuous phase transition…
Gauge-constrained Spinon Complexes Near Deconfined Quantum Criticality
University of Tokyo（东京大学）；Institute of Solid-State Physics, University of Tokyo（东京大学固体物理研究所）；Trans-scale Quantum Science Institute, The University of Tokyo（东京大学跨尺度量子科学研究所）；University of Chongqing（重庆大学）；Department of Physics, University of Chongqing（重庆大学物理学院）
Emergent symmetry is one of the characteristic phenomena in deconfined quantum critical point (DQCP). As its nonequilibrium generalization, the dual dynamic scaling was recently discovered in the nonequilibrium imaginary-time relaxation dynamics in the DQCP of the $J$-$Q_3$ model. In this work, we study the nonequilibrium imaginary-time relaxation dynamics in the $J$-$Q_2$ model, which also hosts a DQCP belonging to the same equilibrium universality class. We not only verify the universality of the dual dynamic scaling at the critical point, but also investigate the breakdown and the vestige o…
It has been proposed that the deconfined criticality in $(2+1)d$ -- the quantum phase transition between a Neel anti-ferromagnet and a valence-bond-solid (VBS) -- may actually be pseudo-critical, in the sense that it is a weakly first-order transition with a generically long correlation length. The underlying field theory of the transition would be a slightly complex (non-unitary) fixed point as a result of fixed points annihilation. This proposal was motivated by existing numerical results from large scale Monte-Carlo simulations as well as conformal bootstrap. However, an actual theory of su…
The phase transition between the valence-bond-solid (VBS) and nematic phases, the so-called deconfined criticality, was investigated for the quantum S=1-spin model on the spatially anisotropic triangular lattice with the biquadratic interaction by means of the numerical diagonalization method. We calculated both VBS- and nematic-order parameters, aiming to clarify the nature of this transition from complementary viewpoints. Simulating the clusters with N \le 20 spins, we estimate the correlation-length critical exponent as ν=0.95(14). We also calculated Fisher's exponent (anomalous dimension) …
The theory of deconfined quantum critical points describes phase transitions at temperature T = 0 outside the standard paradigm, predicting continuous transformations between certain ordered states where conventional theory requires discontinuities. Numerous computer simulations have offered no proof of such transitions, however, instead finding deviations from expected scaling relations that were neither predicted by the DQC theory nor conform to standard scenarios. Here we show that this enigma can be resolved by introducing a critical scaling form with two divergent length scales. Simulatio…
Numerical studies of the Néel to valence-bond solid phase transition in 2D quantum antiferromagnets give strong evidence for the remarkable scenario of deconfined criticality, but display strong violations of finite-size scaling that are not yet understood. We show how to realise the universal physics of the Neel-VBS transition in a 3D classical loop model (this includes the interference effect that suppresses Néel hedgehogs). We use this model to simulate unprecedentedly large systems (of size $L\leq 512$). Our results are compatible with a direct continuous transition at which both order par…
The QED$_3$-Gross-Neveu model is a (2+1)-dimensional U(1) gauge theory involving Dirac fermions and a critical real scalar field. This theory has recently been argued to represent a dual description of the deconfined quantum critical point between Neel and valence bond solid orders in frustrated quantum magnets. We study the critical behavior of the QED$_3$-Gross-Neveu model by means of an epsilon expansion around the upper critical space-time dimension of $D_c^+=4$ up to the three-loop order. Estimates for critical exponents in 2+1 dimensions are obtained by evaluating the different Pade appr…
We study the critical properties of the QED$_3$-Gross-Neveu model with $2N$ flavors of two-component Dirac fermions coupled to a massless scalar field and a U(1) gauge field. For $N=1$, this theory has recently been suggested to be dual to the SU(2) noncompact CP$^1$ model that describes the deconfined phase transition between the Neel antiferromagnet and the valence bond solid on the square lattice. For $N=2$, the theory has been proposed as an effective description of a deconfined critical point between chiral and Dirac spin liquid phases, and may potentially be realizable in spin-$1/2$ syst…
Using the density-matrix renormalization group method for the ground state and excitations of the Shastry- Sutherland spin model, we demonstrate the existence of a narrow quantum spin liquid phase between the previously known plaquette-singlet and antiferromagnetic states. Our conclusions are based on finite-size scaling of excited level crossings and order parameters. Together with previous results on candidate models for deconfined quantum criticality and spin liquid phases, our results point to a unified quantum phase diagram where the deconfined quantum-critical point separates a line of f…
We study the thermodynamic phase transition of a spin Hamiltonian comprising two 3D magnetic sublattices. Each sublattice contains XY spins coupled by the usual bilinear exchange, while spins in different sublattices only interact via biquadratic exchange. This Hamiltonian is an effective model for XY magnets on certain frustrated lattices such as body centered tetragonal. By performing a cluster Monte Carlo simulation, we investigate the crossover from the 3D-XY fixed point (decoupled sublattices) and find a systematic flow toward a first-order transition without a separatrix or a new fixed p…
The deconfined quantum critical point (QCP), separating the Néel and valence bond solid phases in a 2D antiferromagnet, was proposed as an example of $2+1$D criticality fundamentally different from standard Landau-Ginzburg-Wilson-Fisher {criticality}. In this work we present multiple equivalent descriptions of deconfined QCPs, and use these to address the possibility of enlarged emergent symmetries in the low energy limit. The easy-plane deconfined QCP, besides its previously discussed self-duality, is dual to $N_f = 2$ fermionic quantum electrodynamics (QED), which has its own self-duality an…
Quantum information theory and strongly correlated electron systems share a common theme of macroscopic quantum entanglement. In both topological error correction codes and theories of quantum materials (spin liquid, heavy fermion and high-$T_c$ systems) entanglement is implemented by means of an emergent gauge symmetry. Inspired by these connections, we introduce a simple model for fermions moving in the deconfined phase of a $\mathbb Z_2$ gauge theory, by coupling Kitaev's toric code to mobile fermions. This permits us to exactly solve the ground state of this system and map out its phase di…
The criticality of the (2+1)-dimensional S=1 transverse-field Ising model is investigated with the numerical diagonalization method. The scaling behavior is improved by tuning the coupling-constant parameters; the S=1 spin model allows us to incorporate a variety of interactions such as the single-ion anisotropy and the biquadratic interactions. Simulating the clusters with N=6,8,...,20 spins, we estimate the critical indices as 1/ν=1.586(6) and η=0.034(4).
We investigate the ground state phase diagram of an extended Hubbard model with $π$-flux hopping term at half-filling on a square lattice, with unbiased large-scale auxiliary-field quantum Monte Carlo simulations. As a function of interaction strength, there emerges an intermediate phase which realizes two interaction-driven quantum critical points, with the first between the Dirac semimetal and an insulating phase of weak valence bond solid (VBS) order, and the second separating the VBS order and an antiferromagnetic insulating phase. These intriguing quantum critical points are respectively …
Critical bifurcation and deconfined quantum criticality in an interacting cluster Ising chain
Indian Institute of Technology Madras（马德拉斯理工学院）；Center for Quantum Information, Communication and Computation (CQuICC)（量子信息、通信与计算中心）；Karlstad University（卡尔斯特德大学）；Heinrich-Heine-Universität（海因里希·海涅大学）；Ilia State University（伊利亚州立大学）；Andronikashvili Institute of Physics（安德罗尼卡什维利物理研究所）；The Abdus Salam International Centre for Theoretical Physics (ICTP)（阿卜杜斯·萨拉姆国际理论物理中心）
The theory of second order phase transitions is one of the foundations of modern statistical mechanics and condensed matter theory. A central concept is the observable `order parameter', whose non-zero average value characterizes one or more phases and usually breaks a symmetry of the Hamiltonian. At large distances and long times, fluctuations of the order parameter(s) are described by a continuum field theory, and these dominate the physics near such phase transitions. In this paper we show that near second order quantum phase transitions, subtle quantum interference effects can invalidate t…
The $\mathrm{SO}(5)$ Deconfined Phase Transition under the Fuzzy Sphere Microscope: Approximate Conformal Symmetry, Pseudo-Criticality, and Operator Spectrum
Generalizing Deconfined Criticality to 3D $N$-Flavor $\mathrm{SU}(2)$ Quantum Chromodynamics on the Fuzzy Sphere
Wake Forest University（维克森林大学）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）；University of Waterloo（滑铁卢大学）；C. N. Yang Institute for Theoretical Physics, Stony Brook University（石溪大学陈省身理论物理研究所）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）
The conventional Kibble-Zurek mechanism (KZM) describes the driven critical dynamics in the Landau-Ginzburg-Wilson (LGW) spontaneous symmetry-breaking phase transitions. However, whether the KZM is still applicable in the deconfined quantum criticality, which is beyond the LGW paradigm, has not been explored. In this paper, we study the driven critical dynamics near a one-dimensional incarnation of deconfined quantum critical point between a ferromagnetic (FM) phase and a valance-bond-solid (VBS) phase. By investigating the dependence of the density of the topological defects on the driving ra…
As proposed to describe putative continuous phase transitions between two ordered phases, the deconfined quantum critical point (DQCP) goes beyond the prevalent Landau-Ginzburg-Wilson (LGW) paradigm since its critical theory is not expressed in terms of the order parameters characterizing either state, but involves fractionalized degrees of freedom and an emergent symmetry. So far, great efforts have been spent on its equilibrium properties, but the nonequilibrium properties therein are largely unknown. Here we study the nonequilibrium dynamics of the DQCP via the imaginary-time evolution in t…
We investigate quantum impurity problems, where a local magnetic moment is coupled to the spin density of a bosonic environment, leading to bosonic versions of the standard Kondo and Anderson impurity models. In a physical situation, these bosonic environments can correspond either to deconfined spinons in certain classes of Z_2 frustrated antiferromagnets, or to particles in a multicomponent Bose gase (in which case the spin degree of freedom is attributed to hyperfine levels). Using renormalization group techniques, we establish that our impurity models, which feature an exchange interaction…
The Neel magnetization of 2+1 D antiferromagnets is composed of quark-like spin 1/2 constituents, the spinons, as follows from the CP^1 mapping. These quark spinons are confined in both the Neel ordered phase and quantum paramagnetic phases. The confinement in the quantum paramagnetic phase is understood as arising from quantum tunneling events, instantons or hedgehog monopole events. In the present article, we study the approach to the quantum critical point, where the quantum paramagnetic phase ceases to exist. We find that irrespective of the intrinsic spin of the antiferromagnet, instanton…
At sufficiently low temperatures, interacting electron systems tend to develop orders. Exceptions are quantum critical point (QCP) and quantum spin liquid (QSL), where fluctuations prevent the highly entangled quantum matter to an ordered state down to the lowest temperature. While the ramification of these states may have appeared in high-temperature superconductors, ultra-cold atoms, frustrated magnets and quantum Moiré materials, their unbiased presence remain elusive in microscopic two-dimensional lattice models. Here, we show by means of large-scale quantum Monte Carlo simulations of corr…
The quantum $XY$ spin chain with the interactions decaying as a power law $1/r^{1+ σ}$ of the distance between spins $r$ was investigated with the exact diagonalization method. Here, the constituent spin is set to $S=1$, which enables us to incorporate the biquadratic interactions so as to realize the order-disorder transition with the O$(2)$ symmetry maintained. Thereby, in the ordered phase, we resolved the Higgs mass $m_H$ out of the Goldstone-excitation continuum by specifying Higgs-particle's quantum numbers to adequate indices. We then turn to the analysis of the critical amplitude ratio…
The simplest topologically ordered phase in 2+1D is the deconfined phase of $Z_2$ gauge theory, realized for example in the toric code. This phase permits a duality that exchanges electric and magnetic excitations (``$e$'' and ``$m$'' particles). Condensing either particle while the other remains gapped yields a phase transition with 3D Ising exponents. More mysterious, however, is the transition out of the deconfined phase when self-duality symmetry is preserved. If this transition is continuous, which has so far been unclear, then it may be the simplest critical point for which we still lack…
Inspired by our recent works[1, 2] of SU(2) and SU(4) Dirac fermions subjected to plaquette interactions on square lattice, here we extend the large-scale quantum Monte Carlo investigations to the phase digram of correlated Dirac fermions with SU(6) and SU(8) symmetries subjected to the plaquette interaction on the same lattice. From SU(2) to SU(8), the rich phase diagram exhibits a plethora of emerging quantum phases such as the Dirac semimetal, the antiferromagnetic Mott insulator, valence bond solid (VBS) and the Dirac spin liquid and phase transitions including the Gross-Neveu chiral trans…
We suggest the possibility that the two-dimensional SU(2)$_k$ Wess-Zumino-Witten (WZW) theory, which has global SO(4) symmetry, can be continued to $2+ε$ dimensions by enlarging the symmetry to SO$(4+ε)$. This is motivated by the three-dimensional sigma model with SO(5) symmetry and a WZW term, which is relevant to deconfined criticality. If such a continuation exists, the structure of the renormalization group flows at small $ε$ may be fixed by assuming analyticity in $ε$. This leads to the conjecture that the WZW fixed point annihilates with a new, unstable fixed point at a critical dimensio…
Quantum Charge-4e Superconductivity and Deconfined Pseudocriticality in the Attractive SU(4) Hubbard Model
Center for Computational Quantum Physics, Flatiron Institute（平顿研究所计算量子物理中心）；Department of Physics and Engineering Physics, Tulane University（杜兰大学物理与工程物理系）；Institute for Advanced Study, Tsinghua University（清华大学高等研究院）
Progress in understanding symmetry-protected topological (SPT) phases has been greatly aided by our ability to construct lattice models realizing these states. In contrast, a systematic approach to constructing models that realize quantum critical points between SPT phases is lacking, particularly in dimension $d>1$. Here, we show how the recently introduced notion of the pivot Hamiltonian -- generating rotations between SPT phases -- facilitates such a construction. We demonstrate this approach by constructing a spin model on the triangular lattice, which is midway between a trivial and SPT p…
Pseudocriticality in antiferromagnetic spin chains
Indian Institute of Technology Bombay（印度理工学院孟买分校）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；University of Tennessee（田纳西大学）
Lieb-Schultz-Mattis (LSM) theorems provide powerful constraints on the emergibility problem, i.e. whether a quantum phase or phase transition can emerge in a many-body system. We derive the topological partition functions that characterize the LSM constraints in spin systems with $G_s\times G_{int}$ symmetry, where $G_s$ is an arbitrary space group in one or two spatial dimensions, and $G_{int}$ is any internal symmetry whose projective representations are classified by $\mathbb{Z}_2^k$ with $k$ an integer. We then apply these results to study the emergibility of a class of exotic quantum crit…
