arXiv subjects

Xiangjian Qian

Publications and source records attributed to Xiangjian Qian.

At least 19 recordsLinked to original sources

arXiv2026

On the precise boundary of the Néel antiferromagnetic phase in the Shastry-Sutherland model

The ground state phase diagram of the Shastry-Sutherland model remains controversial. In particular, the nature of the transition between the plaquette valence bond solid (PVBS) phase and the Néel antiferromagnetic (AFM) phase is still under debate. While some studies suggest a direct transition between the two phases, others propose the existence of a narrow intermediate quantum spin liquid regime. To address this issue, we perform large-scale Density Matrix Renormalization Group calculations to determine the Néel AFM phase boundary in the Shastry-Sutherland model. By applying staggered boundary pinning fields and directly measuring the bulk staggered magnetization, and through systematic extrapolations with respect to truncation error as well as careful finite-size scaling, we find that the staggered magnetization remains finite across the controversial region $0.78 \lesssim J_{1}/J_{2} \leq 0.81$, which was suggested to host a quantum spin liquid phase in some studies. Together with the previously established consensus placing the PVBS phase boundary at $J_{1}/J_{2} \approx 0.78$, these results provide evidence against the existence of an intermediate quantum spin liquid phase and support a direct PVBS--Néel AFM transition in the Shastry-Sutherland model.

cond-mat.str-el↗

arXiv2026

Dismagicker: Unitary Gate for Non-Stabilizerness Reduction

We introduce the notion of dismagicker: non-Clifford unitary gate designed to reduce the non-stabilizerness (also called magic) of quantum many-body states. Although both entanglement and non-stabilizerness are fundamental quantum resources, they require distinct control strategies. While disentanglers (unitary operations that lower entanglement) are well-established in tensor network methods, analogous concept for non-stabilizerness suppression has been largely missing. In this work, we define dismagicker as non-Clifford unitary operation that actively suppresses non-stabilizerness, steering states toward classically simulatable stabilizer states. We develop optimization method for constructing dismagickers within the Matrix Product States framework. Our numerical results show that the non-stabilizerness reduction procedure, when combined with entanglement reduction steps with Clifford circuits, significantly improves the accuracy for both classical simulation of many-body systems and quantum state preparation on quantum devices. Dismagicker enriches our toolkit for the manipulation of many-body states by unifying non-stabilizerness and entanglement reduction.

quant-ph↗

arXiv2025

Augmenting Density Matrix Renormalization Group with Matchgates and Clifford circuits

Matchgates and Clifford circuits are two types of quantum circuits which can be efficiently simulated classically, though the underlying reasons are quite different. Matchgates are essentially the single particle basis transformations in the Majorana fermion representation which can be easily handled classically, while the Clifford circuits can be efficiently simulated using the tableau method according to the Gottesman-Knill theorem. In this work, we propose a new wave-function ansatz in which matrix product states are augmented with the combination of Matchgates and Clifford circuits (dubbed MCA-MPS) to take advantage of the representing power of all of them. Moreover, the optimization of MCA-MPS can be efficiently implemented within the Density Matrix Renormalization Group method. Our benchmark results on one-dimensional hydrogen chain show that MCA-MPS can improve the accuracy of the ground-state calculation by several orders of magnitude over MPS with the same bond dimension. This new method provides us a useful approach to study quantum many-body systems. The MCA-MPS ansatz also expands our understanding of classically simulatable quantum many-body states.

quant-ph↗

arXiv2025

Disentangling Kitaev Quantum Spin Liquid

In this work, we investigate the Kitaev honeycomb model employing the recently developed Clifford Circuits Augmented Matrix Product States (CAMPS) method. While the model in the gapped phase is known to reduce to the toric code model - whose ground state is entirely constructible from Clifford circuits - we demonstrate that the very different gapless quantum spin liquid (QSL) phase can also be significantly disentangled with Clifford circuits. Specifically, CAMPS simulations reveal that approximately two-thirds of the entanglement entropy in the isotropic point arises from Clifford-circuit contributions, enabling dramatically more efficient computations compared to conventional matrix product state (MPS) methods. Crucially, this finding implies that the Kitaev QSL state retains significant Clifford-simulatable structure, even in the gapless phase with non-abelian anyon excitations when time reversal symmetry is broken. This property not only enhances classical simulation efficiency significantly but also suggests substantial resource reduction for preparing such states on quantum devices. As an application, we leverage CAMPS to study the Kitaev-Heisenberg model and determine the most accurate phase boundary between the anti-ferromagnetic phase and the Kitaev QSL phase in the model. Our results highlight how Clifford circuits can effectively disentangle the intricate entanglement of Kitaev QSLs, opening avenues for efficiently simulating related and similar strongly correlated models.

cond-mat.str-el↗

arXiv2025

Disentangling critical quantum spin chains with Clifford circuits

Clifford circuits can be utilized to disentangle quantum states with polynomial cost, thanks to the Gottesman-Knill theorem. Based on this idea, the Clifford circuits augmented matrix product states (CAMPS) method, which is a seamless integration of Clifford circuits within the density-matrix renormalization group algorithm, was proposed recently and was shown to be able to reduce entanglement in various quantum systems. In this work, we further explore the power of the CAMPS method in critical spin chains described by conformal field theories (CFTs) in the scaling limit. We find that the optimized disentanglers correspond to {\it duality} transformations, which significantly reduce the entanglement entropy in the ground state. For the critical quantum Ising spin chain governed by the Ising CFT with self-duality, the Clifford circuits found by CAMPS coincide with the duality transformation, i.e., the Kramers-Wannier self-duality in the critical Ising chain. It reduces the entanglement entropy by mapping the free conformal boundary condition to the fixed one. In the more general case of the XXZ chain, the CAMPS gives rise to a duality transformation mapping the model to the quantum Ashkin-Teller spin chain. Our results highlight the potential of the framework as a versatile tool for uncovering hidden dualities and simplifying the entanglement structure of critical quantum systems.

quant-ph↗

arXiv2024

Clifford circuits Augmented Matrix Product States for fermion systems

Clifford circuits Augmented Matrix Product States (CAMPS) was recently proposed to leverage the advantages of both Clifford circuits and Matrix Product States (MPS). Clifford circuits can support large entanglement and can be efficiently simulated classically according to the Gottesman-Knill theorem. So in CAMPS, MPS needs only to handle the so-called Non-stabilizerness Entanglement Entropy which significantly improves the simulation accuracy for a given bond dimension. In this work, we generalize CAMPS to study the Fermion system by taking advantage of the Jordan-Wigner transformation which can map the studied Fermion system to a spin system. We benchmark the method on both the spinless $t-V$ model and the spinful Hubbard model. Our test results show significant improvement of the accuracy of CAMPS over MPS, especially when the interactions are strong. Fermionic CAMPS provides a useful tool for the accurate study of many-body fermion systems in the future and has the potential to help resolve long-standing issues.

cond-mat.str-el↗

arXiv2024

Plaquette-type valence bond solid state in the $J_1$-$J_2$ square-lattice Heisenberg model

We utilize Density Matrix Renormalization Group (DMRG) and Fully Augmented Matrix Product States (FAMPS) methods to investigate the Valence Bond Solid (VBS) phase in the $J_1$-$J_2$ square lattice Heisenberg model. To differentiate between the Columnar Valence Bond Solid (CVBS) and Plaquette Valence Bond Solid (PVBS) phases, we introduce an anisotropy $Δ_y$ in the nearest neighboring coupling in the $y$-direction, aiming at detecting the possible spontaneous rotational symmetry breaking in the VBS phase. In the calculations, we push the bond dimension to as large as $D = 25000$ in FAMPS, simulating systems at a maximum size of $14 \times 14$. With a careful extrapolation of the truncation errors and appropriate finite-size scaling, followed by finite $Δ_y$ scaling analysis of the VBS dimer order parameters, we identify the VBS phase as a PVBS type, meaning there is no spontaneous rotational symmetry breaking in the VBS phase. This study not only resolves the long-standing issue of the characterization of the VBS order in the $J_1$-$J_2$ square lattice Heisenberg model but also highlights the capabilities of FAMPS in the study of two-dimensional quantum many-body systems.

cond-mat.str-el↗

arXiv2024

From the Shastry-Sutherland model to the $J_1$-$J_2$ Heisenberg model

We propose a generalized Shastry-Sutherland model which bridges the Shastry-Sutherland model and the $J_1$-$J_2$ Heisenberg model. By employing large scale Density Matrix Renormalization Group and Fully Augmented Matrix Product State calculations, combined with careful finite-size scaling, we find the phase transition between the plaquette valence bond state (PVBS) and Neel anti-ferromagnetic (AFM) phase in the pure Shastry-Sutherland model is a weak first one. This result indicates the existence of an exotic tri-critical point in the PVBS to AFM transition line in the phase diagram, as the transition in the $J_1$-$J_2$ Heisenberg model was previously determined to be continuous. We determine the location of the tri-critical point in the phase diagram at which first-order transition turns to continuous. Our generalized Shastry-Sutherland model provides not only a valuable platform to explore exotic phases and phase transitions but also more realistic description of Shastry-Sutherland materials like SrCu$_2$(BO$_3$)$_2$.

cond-mat.str-el↗

arXiv2024

Parent Hamiltonian for Fully-augmented Matrix Product States

Density matrix renormalization group (DMRG) or matrix product states (MPS) is the most effective and accurate method for studying one-dimensional quantum many-body systems. However, the application of DMRG to two-dimensional systems is not as successful because of the limited entanglement encoded in the wave-function ansatz. The fully augmented matrix product states (FAMPS), introduced recently in [Chin. Phys. Lett. 40, 057102 (2023)], extends MPS formalism to two dimensions and increases the entanglement in the wave-function ansatz, representing a significant advance in the simulation of two-dimensional quantum many-body physics. In the study of one-dimensional systems, the concept of a parent Hamiltonian for MPS has proven pivotal in the understanding of quantum entanglement. In this work, we extend this framework to two-dimensional systems. We illustrate the procedure to construct a two-dimensional Hamiltonian with given FAMPS as its exact ground state (the parent Hamiltonian for FAMPS). Additionally, through numerical simulations, we demonstrate the effectiveness of the algorithm outlined in [Chin. Phys. Lett. 40, 057102 (2023)] in precisely identifying the FAMPS for the constructed parent Hamiltonian. The introduction of FAMPS and its associated parent Hamiltonian provides a useful framework for the future investigations of two-dimensional quantum many-body systems.

cond-mat.str-el↗

arXiv2024

Augmenting Density Matrix Renormalization Group with Clifford Circuits

Density Matrix Renormalization Group (DMRG) or Matrix Product States (MPS) are widely acknowledged as highly effective and accurate methods for solving one-dimensional quantum many-body systems. However, the direct application of DMRG to the study two-dimensional systems encounters challenges due to the limited entanglement encoded in the wave-function ansatz. Conversely, Clifford circuits offer a promising avenue for simulating states with substantial entanglement, albeit confined to stabilizer states. In this work, we present the seamless integration of Clifford circuits within the DMRG algorithm, leveraging the advantages of both Clifford circuits and DMRG. This integration leads to a significant enhancement in simulation accuracy with small additional computational cost. Moreover, this framework is useful not only for its current application but also for its potential to be easily adapted to various other numerical approaches

cond-mat.str-el↗

arXiv2024

Numerical study of bi-layer two-orbital model for La$_{3}$Ni$_{2}$O$_{7}$ on a plaquette ladder

The recently discovered high-$T_c$ superconductivity in La$_{3}$Ni$_{2}$O$_{7}$ with $T_c \approx 80K$ provides another intriguing platform to explore the microscopic mechanism of unconventional superconductivity. In this work, we study a previously proposed bi-layer two-orbital model Hamiltonian for La$_{3}$Ni$_{2}$O$_{7}$ [Y. Shen, et al, Chinese Physics Letters 40, 127401 (2023)] on a plaquette ladder, which is a minimum setup with two-dimensional characteristic. We employ large-scale Density Matrix Renormalization Group calculations to accurately determine the ground state of the model. We determine the density, magnetic structure, and the pairing property of the model. We find that with large effective inter-layer anti-ferromagnetic exchange for the 3$d_{z^2}$ orbital, both spin, charge, and pairing correlation display quasi-long-range behavior, which could be viewed as a precursor of possible true long-range order in the two dimensional limit. Interestingly, sign oscillation for the pairing correlation are observed for both the 3$d_{x^2-y^2}$ and 3$d_{z^2}$ orbitals, indicating the presence of possible pair density wave in the system. Even though we only study the model on a quasi one-dimensional plaquette ladder geometry due to the computational difficulty, the results on the spin, charge, and pairing correlation provide valuable insight in the clarification of the properties of La$_{3}$Ni$_{2}$O$_{7}$ in the future.

cond-mat.str-el↗

arXiv2024

Augmenting Finite Temperature Tensor Network with Clifford Circuits

Recent studies have highlighted the combination of tensor network methods and the stabilizer formalism as a very effective framework for simulating quantum many-body systems, encompassing areas from ground state to time evolution simulations. In these approaches, the entanglement associated with stabilizers is transferred to Clifford circuits, which can be efficiently managed due to the Gottesman-Knill theorem. Consequently, only the non-stabilizerness entanglement needs to be handled, thereby reducing the computational resources required for accurate simulations of quantum many-body systems in tensor network related methods. In this work, we adapt this paradigm for finite temperature simulations in the framework of Time-Dependent Variational Principle, in which imaginary time evolution is performed using the purification scheme. Our numerical results on the one-dimensional Heisenberg model and the two-dimensional $J_1-J_2$ Heisenberg model demonstrate that Clifford circuits can significantly improve the efficiency and accuracy of finite temperature simulations for quantum many-body systems. This improvement not only provides a useful tool for calculating finite temperature properties of quantum many-body systems, but also paves the way for further advancements in boosting the finite temperature tensor network calculations with Clifford circuits and other quantum circuits.

quant-ph↗

arXiv2024

Non-stabilizerness Entanglement Entropy: a measure of hardness in the classical simulation of quantum many-body systems

Classical and quantum states can be distinguished by entanglement entropy, which can be viewed as a measure of quantum resources. Entanglement entropy also plays a pivotal role in understanding computational complexity in simulating quantum systems. However, stabilizer states formed solely by Clifford gates can be efficiently simulated with the tableau algorithm according to the Gottesman-Knill theorem, although they can host large entanglement entropy. In this work, we introduce the concept of non-stabilizerness entanglement entropy which is basically the minimum residual entanglement entropy for a quantum state by excluding the contribution from Clifford circuits. It can serve as a new practical and better measure of difficulty in the classical simulation of quantum many-body systems. We discuss why it is a better criterion than previously proposed metrics such as Stabilizer Rényi Entropy. We also show numerical results of non-stabilizerness entanglement entropy with concrete quantum many-body models. The concept of non-stabilizerness entanglement entropy expands our understanding of the ``hardness`` in the classical simulation of quantum many-body systems.

quant-ph↗

arXiv2024

Atomic-Scale Imaging of Fractional Spinon Quasiparticles in Open-Shell Triangulene Spin-$\frac{1}{2}$ Chains

The emergence of spinon quasiparticles, which carry spin but lack charge, is a hallmark of collective quantum phenomena in low-dimensional quantum spin systems. While the existence of spinons has been demonstrated through scattering spectroscopy in ensemble samples, real-space imaging of these quasiparticles within individual spin chains has remained elusive. In this study, we construct individual Heisenberg antiferromagnetic spin-$\frac{1}{2}$ chains using open-shell [2]triangulene molecules as building blocks. Each [2]triangulene unit, owing to its sublattice imbalance, hosts a net spin-$\frac{1}{2}$ in accordance with Lieb's theorem, and these spins are antiferromagnetically coupled within covalent chains with a coupling strength of $J = 45$ meV. Through scanning tunneling microscopy and spectroscopy, we probe the spin states, excitation gaps, and their spatial excitation weights within covalent spin chains of varying lengths with atomic precision. Our investigation reveals that the excitation gap decreases as the chain length increases, extrapolating to zero for long chains, consistent with Haldane's gapless prediction. Moreover, inelastic tunneling spectroscopy reveals an m-shaped energy dispersion characteristic of confined spinon quasiparticles in a one-dimensional quantum box. These findings establish a promising strategy for exploring the unique properties of excitation quasiparticles and their broad implications for quantum information.

cond-mat.mtrl-sci↗

arXiv2024

Clifford Circuits Augmented Time-Dependent Variational Principle

The recently proposed Clifford Circuits Augmented Matrix Product States (CA-MPS) (arXiv:2405.09217) seamlessly augments Density Matrix Renormalization Group with Clifford circuits. In CA-MPS, the entanglement from stabilizers is transferred to the Clifford circuits which can be easily handled according to the Gottesman-Knill theorem. As a result, MPS needs only to deal with the non-stabilizer entanglement, which largely reduce the bond dimension and the resource required for the accurate simulation of many-body systems. In this work, we generalize CA-MPS to the framework of Time-Dependent Variational Principle (TDVP) for time evolution simulations. In this method, we apply Clifford circuits to the resulting MPS in each TDVP step with a two-site sweeping process similar as in DMRG, aiming at reducing the entanglement entropy in the MPS, and the Hamiltonian is transformed accordingly using the chosen Clifford circuits. Similar as in CA-MPS, the Clifford circuits doesn't increase the number of terms in the Hamiltonian which makes the overhead very small in the new method. We test this method in both XXZ chain and two dimensional Heisenberg model. The results show that the Clifford circuits augmented TDVP method can reduce the entanglement entropy in the time evolution process and hence makes the simulation reliable for longer time. The Clifford circuits augmented Time-Dependent Variational Principle provides a useful tool for the simulation of time evolution process of many-body systems in the future.

cond-mat.str-el↗

arXiv2024

Absence of spin liquid phase in the $J_1-J_2$ Heisenberg model on the square lattice

We perform an in-depth investigation of the phase diagram of the $J_1-J_2$ Heisenberg model on the square lattice. We take advantage of Density Matrix Renormalization Group and Fully-Augmented Matrix Product States methods and reach unprecedented accuracy with large bond dimensions. We utilize excited-level crossing analysis to pinpoint the phase transition points. It was believed before that there exists a narrow spin liquid phase sandwiched by the Néel antiferromagnetic (AFM) and valence bond solid (VBS) phases. Through careful finite size scaling of the level crossing points, we find a direct phase transition between the Néel AFM and VBS phases at $J_2/J_1 = 0.535(3)$, suggesting the absence of an intermediate spin liquid phase. We also provide accurate results for ground state energies for a variety of sizes, from which we find that the transition between the Néel AFM and VBS phases is continuous. These results indicate the existence of a deconfined quantum critical point at $J_2/J_1 = 0.535(3)$ in the model. From the crossing of the first derivative of the energies with $J_2$ for different sizes, we also determine the precise location of the first order phase transition between the VBS and stripe AFM phases at $J_2/J_1=0.610(5)$.

cond-mat.str-el↗

arXiv2024

The ground state of electron-doped $t-t'-J$ model on cylinders

We perform a comprehensive study of the electron-doped $t-t'-J$ model on cylinders with Density Matrix Renormalization Group (DMRG). We adopt both periodic and anti-periodic boundary conditions along the circumference direction to explore the finite size effect. We study doping levels of $1/6$, $1/8$, and $1/12$ which represent the most interesting region in the phase diagram of electron-doped cuprates. We find that for width-4 and 6 systems, the ground state for fixed doping switches between anti-ferromagnetic Neel state and stripe state under different boundary conditions and with system widths, indicating the presence of large finite size effect in the $t-t'-J$ model. We also have a careful analysis of the $d$-wave pairing correlations which also changes quantitatively with boundary conditions and widths of the system. However, the pairing correlations are enhanced when the system becomes wider for all dopings, suggesting the existence of possible long-ranged superconducting order in the thermodynamic limit. The width-8 results are found to be dependent on the starting state in the DMRG calculation for the kept states we can reach. For width-8 system only Neel (stripe) state can be stabilized in DMRG calculation for $1/12$ ($1/6$) doping, while both stripe and Neel states are stable in the DMRG sweep for $1/8$ doping, regardless of the boundary conditions. These results indicate that $1/8$ doping is likely to lie in the boundary of a phase transition between the Neel phase with lower doping and the stripe phase with higher doping, consistent with the previous study. The sensitivity of ground state on boundary conditions and size observed in this work is similar to that in the $t'$- Hubbard model.

cond-mat.str-el↗

arXiv2023

On the Magnetization of the $120^\circ$ order of the Spin-1/2 Triangular Lattice Heisenberg Model: a DMRG revisit

We revisit the issue about the magnetization of the $120^\circ$ order in the spin-1/2 triangular lattice Heisenberg model (TLHM) with Density Matrix Renormalization Group (DMRG). The accurate determination of the magnetization of this model is challenging for numerical methods and its value exhibits substantial disparities across various methods. We perform a large-scale DMRG calculation of this model by employing bond dimension as large as $D = 24000$ and by studying the system with width as large as $L_\mathrm{y} = 12$. With careful extrapolation with truncation error and suitable finite size scaling, we give a conservative estimation of the magnetization as $M_0 = 0.208(8)$. The ground state energy per site we obtain is $E_g = -0.5503(8)$. Our results provide valuable benchmark values for the development of new methods in the future.

cond-mat.str-el↗