arXiv subjects

M. P. Qin

Publications and source records attributed to M. P. Qin.

13 recordsLinked to original sources

arXiv2026

The evolution of pairing correlation with $3d_{z^{2}}$ electron filling in a bilayer two-orbital model for La$_3$Ni$_2$O$_7$

The discovery of high-${T_c}$ superconductivity in pressurized bilayer nickelate La$_3$Ni$_2$O$_7$ presents a new arena for exploring unconventional pairing mechanisms. A pivotal yet unresolved issue is the specific role of the $3d_{z^{2}}$ orbital of Ni. While its inter-layer super-exchange antiferromagnetic coupling is widely considered crucial for superconductivity, the role of its itinerancy remains undetermined. Early studies showed that the superconductivity is accompanied by the emergence of a small Fermi pocket of the $3d_{z^{2}}$ orbitals. However, recent experiments show controversial results on the role of the $3d_{z^{2}}$ Fermi pocket on superconductivity. Motivated by these experimental results, we investigate an effective bilayer two-orbital model for La$_3$Ni$_2$O$_7$ using density-matrix renormalization group (DMRG) on a minimal one-dimensional geometry. By systematically varying the $3d_{z^{2}}$ orbital filling from $1/12$ doping to half-filling, we observe a pronounced suppression of superconducting correlations near half-filling. Our results demonstrate the itinerancy of $3d_{z^{2}}$ orbital is favorable for the pairing in the bilayer two-orbital model for La$_3$Ni$_2$O$_7$. Moreover, we observe that the pairing correlation is enhanced in regions where charge fluctuations are large, suggesting a competition between charge order and superconductivity in the model.

cond-mat.str-el↗

arXiv2015

Probing the Hofstadter butterfly with the quantum oscillation of magnetization

We have developed a different quantum transfer matrix method to accurately determine thermodynamic properties of the Hofstadter model. This method resolves a technical problem which is intractable by other methods and makes the calculation of physical quantities of the Hofstadter model in the thermodynamic limit at finite temperatures feasible. It is shown that the quantum correction to the de Haas-van Alphen (dHvA) oscillation of magnetization bears the energy structure of Hofstadter butterfly. The measurement of this quantum correction, which can be materialized on the superlattice or cold atom systems, can reveal unambiguously the Hofstadter fractal energy spectrum.

cond-mat.str-el↗

arXiv2014

Partial long-range order in antiferromagnetic Potts models

The Potts model plays an essential role in classical statistical mechanics, illustrating many fundamental phenomena. One example is the existence of partially long-range-ordered states, in which some degrees of freedom remain disordered. This situation may arise from frustration of the interactions, but also from an irregular but unfrustrated lattice structure. We study partial long-range order in a range of antiferromagnetic $q$-state Potts models on different two-dimensional lattices and for all relevant values of $q$. We exploit the power of tensor-based numerical methods to evaluate the partition function of these models and hence to extract the key thermodynamic properties -- entropy, specific heat, magnetization, and susceptibility -- giving deep insight into the phase transitions and ordered states of each system. Our calculations reveal a range of phenomena related to partial ordering, including different types of entropy-driven phase transition, the role of lattice irregularity, very large values of the critical $q_c$, and double phase transitions.

cond-mat.stat-mech↗

arXiv2013

Controlling sign problems in spin models using tensor renormalization

We consider the sign problem for classical spin models at complex $β=1/g_0^2$ on $L\times L$ lattices. We show that the tensor renormalization group method allows reliable calculations for larger Im$β$ than the reweighting Monte Carlo method. For the Ising model with complex $β$ we compare our results with the exact Onsager-Kaufman solution at finite volume. The Fisher zeros can be determined precisely with the TRG method. We check the convergence of the TRG method for the O(2) model on $L\times L$ lattices when the number of states $D_s$ increases. We show that the finite size scaling of the calculated Fisher zeros agrees very well with the Kosterlitz-Thouless transition assumption and predict the locations for larger volume. The location of these zeros agree with Monte Carlo reweighting calculation for small volume. The application of the method for the O(2) model with a chemical potential is briefly discussed.

hep-lat↗

arXiv2013

Tensor renormalization group study of classical XY model on the square lattice

Using the tensor renormalization group method based on the higher-order singular value decom- position, we have studied the thermodynamic properties of the continuous XY model on the square lattice. The temperature dependence of the free energy, the internal energy and the specific heat agree with the Monte Carlo calculations. From the field dependence of the magnetic susceptibility, we find the Kosterlitz-Thouless transition temperature to be 0.8921 \pm 0.0019, consistent with the Monte Carlo as well as the high temperature series expansion results. At the transition temperature, the critical exponent δis estimated as 14.5, close to the analytic value by Kosterlitz.

cond-mat.stat-mech↗

arXiv2013

Exact blocking formulas for spin and gauge models

Using the example of the two-dimensional (2D) Ising model, we show that in contrast to what can be done in configuration space, the tensor renormalization group (TRG) formulation allows one to write exact, compact, and manifestly local blocking formulas and exact coarse grained expressions for the partition function. We argue that similar results should hold for most models studied by lattice gauge theorists. We provide exact blocking formulas for several 2D spin models (the O(2) and O(3) sigma models and the SU(2) principal chiral model) and for the 3D gauge theories with groups Z_2, U(1) and SU(2). We briefly discuss generalizations to other groups, higher dimensions and practical implementations.

hep-lat↗

arXiv2013

Partial order in Potts models on the generalized decorated square lattice

We explore the Potts model on the generalized decorated square lattice, with both nearest (J1) and next-neighbor (J2) interactions. Using the tensor renormalization-group method augmented by higher-order singular value decompositions, we calculate the spontaneous magnetization of the Potts model with q = 2, 3, and 4. The results for q = 2 allow us to benchmark our numerics using the exact solution. For q = 3, we find a highly degenerate ground state with partial order on a single sublattice, but with vanishing entropy per site, and we obtain the phase diagram as a function of the ratio J2=J1. There is no finite-temperature transition for the q = 4 case when J1 = J2, but the magnetic susceptibility diverges as the temperature goes to zero, showing that the model is critical at T = 0.

cond-mat.stat-mech↗

arXiv2012

The Quantum Torus Chain

We introduce a new set of one dimensional quantum lattice models which we refer to as The quantum torus chain. These models have discrete global symmetry, and projective on-site representations. They possess an integer-valued parameter which controls the presence or absence of frustration. Depending on whether this parameter is even or odd these models either exhibit gapped symmetry breaking phases with isolated critical points, or gapped symmetry breaking phases separated by gapless phases. We discuss the property of these phases and phase transitions for two special values of the parameter and point out many open problems

cond-mat.str-el↗

arXiv2012

Coarse-graining renormalization by higher-order singular value decomposition

We propose a novel coarse graining tensor renormalization group method based on the higher-order singular value decomposition. This method provides an accurate but low computational cost technique for studying both classical and quantum lattice models in two- or three-dimensions. We have demonstrated this method using the Ising model on the square and cubic lattices. By keeping up to 16 bond basis states, we obtain by far the most accurate numerical renormalization group results for the 3D Ising model. We have also applied the method to study the ground state as well as finite temperature properties for the two-dimensional quantum transverse Ising model and obtain the results which are consistent with published data.

cond-mat.stat-mech↗

arXiv2012

Plaquette order and deconfined quantum critical point in the spin-1 bilinear-biquadratic Heisenberg model on the honeycomb lattice

We have precisely determined the ground state phase diagram of the quantum spin-1 bilinear-biquadratic Heisenberg model on the honeycomb lattice using the tensor renormalization group method. We find that the ferromagnetic, ferroquadrupolar, and a large part of the antiferromagnetic phases are stable against quantum fluctuations. However, around the phase where the ground state is antiferroquadrupolar ordered in the classical limit, quantum fluctuations suppress completely all magnetic orders, leading to a plaquette order phase which breaks the lattice symmetry but preserves the spin SU(2) symmetry. On the evidence of our numerical results, the quantum phase transition between the antiferromagnetic phase and the plaquette phase is found to be either a direct second order or a very weak first order transition.

cond-mat.str-el↗

arXiv2011

Partial order and finite-temperature phase transitions in Potts models on irregular lattices

We evaluate the thermodynamic properties of the 4-state antiferromagnetic Potts model on the Union- Jack lattice using tensor-based numerical methods. We present strong evidence for a previously unknown, "entropy-driven," finite-temperature phase transition to a partially ordered state. From the thermodynamics of Potts models on the diced and centered diced lattices, we propose that finite-temperature transitions and partially ordered states are ubiquitous on irregular lattices.

cond-mat.str-el↗

arXiv2010

Translation invariant tensor product states in a finite lattice system

We show that the matrix (or more generally tensor) product states in a finite translation invariant system can be accurately constructed from the same set of local matrices (or tensors) that are determined from an infinite lattice system in one or higher dimensions. This provides an efficient approach for studying translation invariant tensor product states in finite lattice systems. Two methods are introduced to determine these size-independent local tensors.

cond-mat.str-el↗

arXiv2010

Fractality of Hofstadter Butterfly in Specific Heat Oscillation

We calculate thermodynamical properties of the Hofstadter model using a recently developed quantum transfer matrix method. We find intrinsic oscillation features in specific heat that manifest the fractal structure of the Hofstadter butterfly. We also propose experimental approaches which use specific heat as an access to detect the Hofstadter butterfly.

cond-mat.str-el↗