Yuhai Liu, Zhenjiu Wang, Toshihiro Sato, Wenan Guo, Fakher F. Assaad
We consider fermions on a honeycomb lattice supplemented by a spin invariant interaction that dynamically generates a quantum spin Hall insulator. This lattice model provides an instance of Gross-Neveu Heisenberg criticality, as realized for example by the Hubbard model on the honeycomb lattice. Using auxiliary field quantum Monte Carlo simulations we show that we can compute with unprecedented precision susceptibilities of the order parameter. In O(N) Gross-Neveu transitions, the anomalous dimension of the bosonic mode grows as a function of N such that in the large-N limit it is of particular importance to consider susceptibilities rather than equal time correlations so as to minimize contributions from the background. For the N=3 case, we obtain $1/ν=1.11(4)$, $η_φ=0.80(9)$, and $η_ψ=0.29(2)$ for respectively the correlation length exponent, bosonic and fermionic anomalous dimensions.
Yuhai Liu, Zhenjiu Wang, Toshihiro Sato, Martin Hohenadler, Chong Wang, Wenan Guo, Fakher F. Assaad
The discovery that spin-orbit coupling can generate a new state of matter in the form of quantum spin-Hall (QSH) insulators has brought topology to the forefront of condensed matter physics. While QSH states from spin-orbit coupling can be fully understood in terms of band theory, fascinating many-body effects are expected if the state instead results from interaction-generated symmetry breaking. In particular, topological defects of the corresponding order parameter provide a route to exotic quantum phase transitions. Here, we introduce a model in which the condensation of skyrmion defects in an interaction-generated QSH insulator produces a superconducting (SC) phase. Because vortex excitations of the latter carry a spin-$1/2$ degree of freedom numbers, the SC order may be understood as emerging from a gapless spin liquid normal state. The QSH-SC transition is an example of a deconfined quantum critical point (DQCP), for which we provide an improved model with only a single length scale that is accessible to large-scale quantum Monte Carlo simulations.
Ye Ling, Yuting Wang, Wenan Guo, Yuhai Liu
The sign-problematic generalized Baxter-Wu (GBW) model with asymmetric complex couplings is mapped onto a one-dimensional quantum model. Utilizing the model's exactly known critical properties, we study the relation between the conventional and the modified average signs and the phase transitions in the GBW model. We find that the average sign develops a negative peak near the critical point, but it is not a unique indicator of phase transition, as similar features can appear in non-critical regions. While the average modified sign provides a viable probe for the phase transition, the practical effectiveness of this method is limited by the exponential scaling of computational cost with the system's volume. We propose that the universal properties of the original model can be investigated through simulating the related reference model, based on the universality assumption. Using finite-size scaling analysis based on Monte Carlo simulations, we confirm the validity of this method, which thereby provides a novel framework for investigating phase transitions in systems plagued by the sign problem.
Disha Hou, Yuhai Liu, Toshihiro Sato, Wenan Guo, Fakher F. Assaad, Zhenjiu Wang
The quantum spin Hall state can be understood in terms of spontaneous O(3) symmetry breaking. Topological skyrmion configurations of the O(3) order parameter vector carry a charge 2e, and as shown previously, when they condense, a superconducting state is generated. We show that this topological route to superconductivity survives easy-plane anisotropy. Upon reducing the O(3) symmetry to O(2)$\times$ Z$_2$, skyrmions give way to merons that carry a unit charge. On the basis of large-scale auxiliary field quantum Monte Carlo simulations, we show that at the particle-hole symmetric point, we can trigger a continuous and direct transition between the quantum spin Hall state and s-wave superconductor by condensing pairs of merons. This statement is valid in both strong and weak anisotropy limits. Our results can be interpreted in terms of an easy-plane deconfined quantum critical point. However, in contrast to the previous studies in quantum spin models, our realization of this quantum critical point conserves $U(1)$ charge, such that skyrmions are conserved.
Yuhai Liu, Toshihiro Sato, Disha Hou, Zhenjiu Wang, Wenan Guo, Fakher F. Assaad
Topology and anomalies lead to edge modes that can interact with critical bulk fluctuations. To study this setup, pertaining to boundary criticality, we consider a model exhibiting a deconfined quantum critical point (DQCP) between a dynamically generated quantum spin Hall state (i.e.a topological Mott insulator) and an s-wave superconductor. For the topological Mott insulator, the bulk Goldstone modes are shown to be irrelevant at the helical Luttinger liquid fixed points. The deconfined quantum critical point is an instance of an emergent anomaly, and we observe a sharp localized edge state at this point. The sharpness of the edge mode is consistent with an ordinary phase in which electronic edge modes decouple from critical edge bosonic fluctuations. At the DQCP, the scaling dimension of the edge electron shows a jump, a feature argued to be a signature of the emergent anomaly. Our results are based on large-scale auxiliary-field quantum Monte Carlo simulations.We also carry out calculations for the Kane-Mele-Hubbard model to confirm spectral features of the ordinary and extraordinary-log phases in the vicinity of the bulk critical point.
Martin Hohenadler, Yuhai Liu, Toshihiro Sato, Zhenjiu Wang, Wenan Guo, Fakher F. Assaad
Thermodynamic and dynamical properties of a model of Dirac fermions with a deconfined quantum critical point (DQCP) separating an interaction-generated quantum spin-Hall insulator from an s-wave superconductor [Nature Comm.~{\bf 10}, 2658 (2019)] are studied by quantum Monte Carlo simulations. Inside the deconfined quantum critical region bound by the single-particle gap, spinons and spinless charge-2e skyrmions emerge. Since the model conserves total spin and charge, and has a single length scale, these excitations lead to a characteristic linear temperature dependence of the uniform spin and charge susceptibilities. At the DQCP, the order parameter dynamic structure factors show remarkable similarities that support emergent Lorentz symmetry. Above a critical temperature, superconductivity is destroyed by the proliferation of spin-1/2 vortices.
Zhenjiu Wang, Yuhai Liu, Toshihiro Sato, Martin Hohenadler, Chong Wang, Wenan Guo, Fakher F. Assaad
A unique property of a dynamically generated quantum spin Hall state are Goldstone modes that correspond to the long-wavelength fluctuations of the spin-orbit coupling order parameter whose topological Skyrmion excitations carry charge 2$e$. Within the model considered here, upon varying the chemical potential, we observe two transitions: An s-wave superconducting order parameter develops at a critical chemical potential $μ_{c1}$, corresponding to the excitation gap of pairs of fermions, and at $μ_{c2}$ the SO(3) order parameter of the quantum spin Hall state vanishes. Using negative-sign-free, large-scale quantum Monte Carlo simulations, we show that $μ_{c1}=μ_{c2}$ within our accuracy -- we can resolve dopings away from half filling down to $δ= 0.0017$. The length scale associated with the fluctuations of the quantum spin Hall order parameter grows down to our lowest doping, suggesting either a continuous or a weakly first-order transition. Contrary to mean-field expectations, the doping versus chemical potential curve is not linear, indicating a dynamical critical exponent $z > 2$ if the transition is continuous.
Yaozheng Zhang, Wei Wang, Jie Kong, Jiehan Zhou, Xianwei Zhang, Huanqing Cui, Han Bao, Yuhai Liu
The increasing adoption of large language models (LLMs) on heterogeneous computing platforms poses significant challenges to achieving high inference efficiency. To address these efficiency bottlenecks across diverse platforms, this paper proposes Opt4GPTQ, a practical optimization method designed for 4-bit GPTQ quantized LLMs inference on heterogeneous AI accelerators. Built upon the vLLM serving system, Opt4GPTQ integrates three platform-level optimization strategies: Shared Memory Buffering Optimization (SMB-Opt), which caches frequently accessed data in shared memory and employs single-threaded writes; Vectorized Memory Loading Optimization (VML-Opt), which utilizes vectorized memory operations for efficient data loading; and Inline Assembly Optimization (ILA-Opt), which directly leverages hardwarenative vector half-precision addition and fused multiply-accumulate instructions. Experimental results show that Opt4GPTQ effectively improves performance across various models while maintaining original model accuracy, achieving throughput gains of up to 84.42%. This work highlights the critical role of platformlevel engineering in enabling efficient LLMs inference on emerging architectures and provides valuable methodologies for future heterogeneous platform adaptation.
Xiaofeng Qian, Youjin Deng, Yuhai Liu, Wenan Guo, Henk W. J. Bloete
We investigate the two-dimensional $q=3$ and 4 Potts models with a variable interaction range by means of Monte Carlo simulations. We locate the phase transitions for several interaction ranges as expressed by the number $z$ of equivalent neighbors. For not too large $z$, the transitions fit well in the universality classes of the short-range Potts models. However, at longer ranges the transitions become discontinuous. For $q=3$ we locate a tricritical point separating the continuous and discontinuous transitions near $z=80$, and a critical fixed point between $z=8$ and 12. For $q=4$ the transition becomes discontinuous for $z > 16$. The scaling behavior of the $q=4$ model with $z=16$ approximates that of the $q=4$ merged critical-tricritical fixed point predicted by the renormalization scenario.
Jie Kong, Junxiang Zhang, Jiheng Xu, Yalong Li, Shouhua Zhang, Jiehan Zhou, Yuhai Liu, Peng Liang, Quan Zhang, Luohan Jiang
In the field of deep learning, traditional attention mechanisms face significant challenges related to high computational complexity and large memory consumption when processing long sequence data. To address these limitations, we propose Opt-GPTQ, an optimized Gradient-based Post Training Quantization (GPTQ) combining the Grouped Query Attention (GQA) mechanism with paging memory management, optimizing the traditional Multi-Head Attention (MHA) mechanism by grouping query heads and sharing key-value vectors. Optimized GQA (Opt-GQA) effectively reduces computational complexity, minimizes memory fragmentation, and enhances memory utilization for large-scale models. Opt-GPTQ is optimized for Data Center Units (DCUs) and integrated into the vLLM model to maximize hardware efficiency. It customizes GPU kernels to further enhance attention computation by reducing memory access latency and boosting parallel computing capabilities. Opt-GQA integrates Attention with Linear Biases (ALiBi) to reduce overhead and enhance long-sequence processing. Experimental results show that Opt-GPTQ significantly reduces computation time and memory usage while improving model performance.
Toshihiro Sato, Zhenjiu Wang, Yuhai Liu, Disha Hou, Martin Hohenadler, Wenan Guo, Fakher F. Assaad
We introduce a model of Dirac fermions in 2+1 dimensions with a semimetallic, a quantum spin-Hall insulating (QSHI), and an s-wave superconducting (SSC) phase. The phase diagram features a multicritical point at which all three phases meet as well as a QSHI-SSC deconfined critical point. The QSHI and SSC orders correspond to mutually anti-commuting mass terms of the Dirac Hamiltonian. Based on this algebraic property, SO(5) symmetric field theories have been put forward to describe both types of critical points. Using quantum Monte Carlo simulations, we directly study the operator that rotates between QSHI and SSC states. The results suggest that it commutes with the low-energy effective Hamiltonian at criticality but has a gap in the ordered phases. This implies an emergent SO(5) symmetry at both the multicritical and the deconfined critical points.
Xiaodong Jin, Yuhai Liu, Rubem Mondaini, Marcos Rigol
We study the superconductor-insulator transition (SIT) in the ground state of the attractive honeycomb Hubbard model in the presence of a staggered potential (a mass term), using a combination of unbiased computational methods, namely, exact diagonalization and quantum Monte Carlo simulations. We probe the nature of the lowest-energy charge excitations across the SIT and show that they are bosonic, as inferred (and shown in the strongly interacting regime) in a previous study of the same model in the square lattice. Increasing the strength of the staggered potential leads to a crossover in which bosonic low-energy excitations give way to fermionic ones within the insulating phase. We also show that the SIT belongs to the 3$d$-XY universality class, like in its square lattice counterpart. The robustness of our results in these two lattice geometries supports the expectation that our findings are universal for SITs in clean systems.
Disha Hou, Yuhai Liu, Toshihiro Sato, Fakher F. Assaad, Wenan Guo, Zhenjiu Wang
We carry out large-scale quantum Monte Carlo simulations of a candidate field theory for the onset of superconductivity in magic-angle twisted bilayer graphene. The correlated insulating state at charge neutrality spontaneously breaks U(1) Moiré valley symmetry. Owing to the topological nature of the bands, skyrmion defects of the order parameter carry charge $2e$ and condense upon doping. In our calculations we encode the U(1) symmetry by an internal degree of freedom such that it is not broken upon lattice regularization. Furthermore, the skyrmion carries the same charge. The nature of the doping-induced phase transitions depends on the strength of the easy-plane anisotropy that reduces the SU(2) valley symmetry to U(1) $\times \mathbb{Z}_2 $. For large anisotropy, we observe two distinct transitions separated by phase coexistence. While the insulator to superconducting transition is of mean-field character, the U(1) transition is consistent with three-dimensional XY criticality. Hence, the coupling between the gapless charge excitations of the superconducting phase and the XY order parameter is irrelevant. At small anisotropy, we observe a first-order transition characterized by phase separation.