arXiv subjects

Mingpu Qin

Publications and source records attributed to Mingpu Qin.

At least 37 records · Page 2Linked to original sources

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

Effective bi-layer model Hamiltonian and density-matrix renormalization group study for the high-Tc superconductivity in La$_{3}$Ni$_{2}$O$_{7}$ under high pressure

High-Tc superconductivity with possible $T_{c}\approx 80K$ has been reported in the single crystal of $\text{La}_{3}\text{Ni}_{2}\text{O}_{7}$ under high pressure. Based on the electronic structure given from the density functional theory calculations, we propose an effective bi-layer model Hamiltonian including both $3d_{z^{2}}$ and $3d_{x^{2}-y^{2}}$ orbital electrons of the nickel cations. The main feature of the model is that the $3d_{z^{2}}$ electrons form inter-layer $σ$-bonding and anti-bonding bands via the apical oxygen anions between the two layers, while the $3d_{x^{2}-y^{2}}$ electrons hybridize with the $3d_{z^{2}}$ electrons within each NiO$_2$ plane. The chemical potential difference of these two orbital electrons ensures that the $3d_{z^{2}}$ orbitals are close to half-filling and the $3d_{x^{2}-y^{2}}$ orbitals are near quarter-filling. The strong on-site Hubbard repulsion of the $3d_{z^{2}}$ orbital electrons gives rise to an effective inter-layer antiferromagnetic spin super-exchange $J$. Applying pressure can self-dope holes on the $3d_{z^{2}}$ orbitals with the same amount of electrons doped on the $3d_{x^{2}-y^{2}}$ orbitals. By performing numerical density-matrix renormalization group calculations on a minimum setup and focusing on the limit of large $J$ and small doping of $3d_{z^{2}}$ orbitals, we find the superconducting instability on both the $3d_{z^{2}}$ and $3d_{x^{2}-y^{2}}$ orbitals by calculating the equal-time spin singlet pair-pair correlation function. Our numerical results have provided useful insights in the high-Tc superconductivity in single crystal La$_3$Ni$_2$O$_7$ under high pressure.

cond-mat.str-el↗

arXiv2023

Reexamining doped two-legged Hubbard ladders

We revisit the ground state of the Hubbard model on 2-legged ladders in this work. We perform DMRG calculation on large system sizes with large kept states and perform extrapolation of DMRG results with truncation errors in the converged region. We find the superconducting correlation exponent $K_{sc}$ extracted from the pair-pair correlation is very sensitive to the position of the reference bond, reflecting a huge boundary effect on it. By systematically removing the effects from boundary conditions, finite sizes, and truncation errors in DMRG, we obtain the most accurate value of $K_{sc}$ and $K_ρ$ so far with DMRG. With these exponents, we confirm that the 2-legged Hubbard model is in the Luther-Emery liquid phase with $K_{sc} \cdot K_ρ= 1$ from tiny doping near half-filling to $1/8$ hole doping. When the doping is increased to $δ\gtrapprox 1/6$, the behaviors of charge, pairing, and spin correlations don't change qualitatively, but the relationship $K_{sc} \cdot K_ρ= 1$ is likely to be violated. With the further increase of the doping to $δ= 1/3$, the quasi long-ranged charge correlation turns to a true long-ranged charge order and the spin gap is closed, while the pair-pair correlation still decays algebraically. Our work provides a standard way to analyze the correlation functions when studying systems with open boundary conditions.

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↗

arXiv2023

Self-consistent optimization of the trial wave-function in constrained path auxiliary field Quantum Monte Carlo using mixed estimators

We propose a new scheme to implement the self-consistent optimization of the trial wave-function in constrained path auxiliary field Quantum Monte Carlo (CP-AFQMC) in the framewok of natural orbitals. In this scheme, a new trial wave-function in the form of Slater determinant is constructed from the CP-AFQMC results by diagonalizing the mixed estimator of the one-body reduced density matrix. We compare two ways (from real and mixed estimators in CP-AFQMC) to calculate the one-body reduced density matrix in the self-consistent process and study the ground state of doped two dimensional Hubbard model to test the accuracy of the two schemes. By comparing the local density, occupancy, and ground state energy we find the scheme in which one-body reduced density matrix is calculated from mixed estimator is computational more efficient and provides more accurate result with less fluctuation. The local densities from mixed estimator scheme agree well with the numerically exact values. This scheme provides a useful tool for the study of strongly correlated electron systems.

cond-mat.str-el↗

arXiv2023

Half-filled stripe to N$\acute e$el antiferromagnetism transition in the $t'$-Hubbard model on honeycomb lattice

We study the ground state of the doped Hubbard model on honeycomb lattice with both nearest ($t$) and next-nearest neighboring hoppings ($t'$) in the small doping and strongly interacting region. Previous study on the model without $t'$ showed the ground state is a half-filled stripe. We employ density matrix renormalization group and extrapolate the results with truncation errors in the converged region. In the $t' < 0$ side, we find the half-filled stripe phase at $t' = 0$ is stable against the frustration of $t'$ until a critical point $-0.4 < t'_c < -0.3$, beyond which the ground state switches to anti-ferromagnetic N$\acute e$el phase with charge modulation. With further increase of $t'$ to $-0.7$, the ground state becomes paramagnetic. In the $t' > 0$ side, the half-filled stripe stretches to $t' \approx 0.7$. We don't find obvious enhancement of pairing for the range of $t'$ studied. We study width-4 cylinders in this work but the results for spin, charge, and pairing correlation agree qualitatively for periodic and anti-periodic boundary conditions in the half-filled stripe and anti-ferromagnetic N$\acute e$el phases, suggesting the results are likely to be representative for true two-dimensional systems. The half-filled stripe to anti-ferromagnetic N$\acute e$el phase transition can be realized on real materials or ultra-cold atom platform.

cond-mat.str-el↗

arXiv2023

The Performance of VQE across a phase transition point in the $J_1$-$J_2$ model on kagome lattice

Variational quantum eigensolver (VQE) is an efficient classical-quantum hybrid method to take advantage of quantum computers in the Noisy Intermediate-Scale Quantum (NISQ) era. In this work we test the performance of VQE by studying the $J_1$-$J_2$ anti-ferromagnetic Heisenberg model on the kagome lattice, which is found to display a first order phase transition at $J_2 / J_1 \approx 0.01$. By comparing the VQE states with the exact diagonalization results, we find VQE energies agree well with the exact values in most region of parameters for the 18-site system we studied. However, near the phase transition point, VQE tends to converge to the excited states when the number of variational parameters is not large enough. For the system studied in this work, this issue can be solved by either increasing the number of parameters or by initializing the parameters with converged values for $J_2/J_1$ away from the phase transition point. Our results provide useful guidance for the practical application of VQE on real quantum computers to study strongly correlated quantum many-body systems.

cond-mat.str-el↗

arXiv2023

Augmenting Density Matrix Renormalization Group with Disentanglers

Density Matrix Renormalization Group (DMRG) and its extensions in the form of Matrix Product States (MPS) are arguably the choice for the study of one dimensional quantum systems in the last three decades. However, due to the limited entanglement encoded in the wave-function ansatz, to maintain the accuracy of DMRG with the increase of the system size in the study of two dimensional systems, exponentially increased resources are required, which limits the applicability of DMRG to only narrow systems. In this work, we introduce a new ansatz in which DMRG is augmented with disentanglers to encode area-law-like entanglement entropy (entanglement entropy supported in the new ansatz scales as $l$ for a $l \times l$ system). In the new method, the $O(D^3)$ low computational cost of DMRG is kept (with an overhead of $O(d^4)$ and $d$ the dimension of the physical degree of freedom). We perform benchmark calculations with this approach on the two dimensional transverse Ising and Heisenberg models. This new ansatz extends the power of DMRG in the study of two-dimensional quantum systems.

cond-mat.str-el↗

arXiv2023

Comparative study of charge order in undoped infinite-layer nickelate superconductors

To understand the microscopic mechanism of the charge order observed in the parent compound of the infinite-layer nickelate superconductors, we consider a minimal three-legged model consisting of a two-legged Hubbard ladder for the Ni $3d_{x^2-y^2}$ electrons and a free conduction electron chain from the rare-earths. With highly accurate density matrix renormalization group calculations, when the chemical potential difference is adjusted to make the Hubbard ladder with $1/3$ hole doping, we find a long-range charge order with period $3$ in the ground state of the model, while the spin excitation has a small energy gap. Moreover, the electron pair-pair correlation has a quasi-long-range behavior, indicating an instability of superconductivity even at half-filling. As a comparison, the same method is applied to a pure two-legged Hubbard model with $1/3$ hole doping in which the period-3 charge order is a quasi-long range one. The difference between them demonstrates that the free electron chain of the three-legged ladder plays the role of a charge reservoir and enhances the charge order in the undoped infinite-layer nickelates.

cond-mat.str-el↗