arXiv subjects

Feng-Feng Song

Publications and source records attributed to Feng-Feng Song.

14 recordsLinked to original sources

arXiv2026

Gaplessness indicator by topologically trivial twisting operators

We propose several general necessary conditions for quantum many-body system in one dimension respecting U(1) symmetry to be gapped. We show that the ground-state expectation value of topologically trivial twisting operators must approach unity in the thermodynamic limit with a certain finite-size scaling. Equivalently, its violation can indicate gaplessness of U(1)-symmetric Hamiltonians. The topological triviality of such a twisting operator enables us to derive infinitely many other gaplessness indicators by static structure factor to any order in real experiments, which are impossible to obtain by earlier topologically nontrivial twisting operators. We also apply analytic and numerical calculations to test the efficiency and consistency of our results.

cond-mat.str-el↗

arXiv2026

$5/9-$Magnetization Plateau and Spin Supersolidity in YCu$_3$(OD)$_{7-x}$Br$_{2+x}$ under Magnetic Fields up to 120~T

We performed high-precision magnetization measurements up to 120~T on three compositions of the newly discovered kagome antiferromagnet YCu$_3$(OD)$_{7-x}$Br$_{2+x}$ (YCOB), revealing a previously unobserved 5/9 fractional magnetization plateau. All YCOB samples with different Br$^-$ concentrations exhibit nearly identical magnetization curves below 60~T, whereas the 5/9 plateau appears at markedly different fields in the ultrahigh-field regime. By modeling the experimental data using tensor-network calculations, we derive the effective spin Hamiltonians for the YCOB family with three spatially anisotropic Heisenberg couplings (the 3$J$-type model), which quantitatively reproduces the measured magnetization processes and captures the composition-dependent evolution of the 5/9 plateau. Furthermore, our theoretical analysis suggests the emergence of a spin supersolid phase in the field window between the 1/3 and 5/9 plateaus, which is sensitive to spin exchange parameters and accounts for the significant variation in the critical fields of the 5/9 plateau observed among different YCOB compositions.

cond-mat.str-el↗

arXiv2025

Variational boundary based tensor network renormalization group

We propose a real-space renormalization group algorithm for accurately coarse-graining two-dimensional tensor networks. The central innovation of our method lies in utilizing variational boundary tensors as a globally optimized environment for the entire system. Based on this optimized environment, we construct renormalization projectors that significantly enhance accuracy. By leveraging the canonical form of tensors, our algorithm maintains the same computational complexity as the original tensor renormalization group (TRG) method, yet achieves higher accuracy than existing approaches that do not incorporate entanglement filtering. Our work offers a practical pathway for extending TRG methods to higher dimensions while keeping computational costs manageable.

cond-mat.stat-mech↗

arXiv2025

Correlated reaction coordinate motion produces non-additive rate enhancement for electron and energy transfer in multi-acceptor structures

Molecular structures with multiple donor, bridge, or acceptor units can display quantum interference effects that influence electron and energy transfer (ET and EnT) rates. Recent experiments found a 4- to 5-fold increase in ET rates for donor-acceptor structures with two acceptors compared to one. This result is surprising: simple classical or quantum analysis suggests a factor of two rate enhancement. We analyze the coupling interactions in multiple acceptor systems and find that rate enhancements beyond additive effects arise from acceptor-acceptor interactions that: 1) shift the reaction free energy, 2) change the donor-acceptor couplings, and 3) alter the reaction-coordinate motion. Consideration of these effects explains the observed rates in multi-acceptor systems and suggests strategies to tailor energy and electron transfer kinetics.

physics.chem-ph↗

arXiv2025

Superfluid dome in the spatially modulated two-dimensional XY model

In strongly correlated electron systems, superconductivity and charge density waves often coexist in close proximity, suggesting a deeper relationship between these competing phases. Recent research indicates that these orders can intertwine, with the superconducting order parameter coupling to modulations in the electronic density. To elucidate this interplay, we study a two-dimensional XY model with a periodic modulation of the coupling strength in one spatial direction. Using a combination of tensor network methods and Monte Carlo simulations, we reveal a non-monotonic, dome-like dependence of $T_c$ on the modulation wavelength, with the peak $T_c$ shifting to longer wavelengths as the modulation strength grows. The origin of this phenomenon is traced back to an effective pinning of vortices in the valleys of the modulation, confirmed by a comparison to modulated $q$-state clock models. These findings shed new light on the phase behavior of intertwined superconducting and charge-ordered states, offering a deeper understanding of their complex interactions.

cond-mat.supr-con↗

arXiv2025

Phase coherence of charge-$6e$ superconductors via a frustrated Kagome XY antiferromagnet

Recent experimental evidence for the charge-$6e$ condensed phase in kagome superconductors has generated significant interest. We investigate the unconventional superconductivity in the kagome superconductor $\mathrm{CsV_3Sb_5}$, focusing on the emergence of charge-$6e$ superconductivity (SC) at temperatures higher than the conventional charge-$2e$ SC state. By modeling the phase coherence of the SC order parameter using a frustrated antiferromagnetic XY model on an emergent kagome lattice, we show that the condensation of fractional vortices with $1/3$ vorticity stabilizes phase coherence in $\exp(i3\theta)$, giving rise to the charge-$6e$ SC state. Using a tensor network approach tailored for frustrated spin systems, we identify a Berezinskii-Kosterlitz-Thouless transition at $T_c/J \simeq 0.075$, where the unbinding of $1/3$ fractional vortex-antivortex pairs transforms the system from the charge-$6e$ SC phase to the normal phase. Below $T_c$, the $1/3$ fractional vortex correlations exhibit power-law decay, while the integer vortex correlations decay exponentially, reflecting the dominance of charge-$6e$ SC in the absence of charge-$2e$ SC. Our results provide a theoretical understanding of the charge-$6e$ SC in two-dimensional kagome superconductors, emphasizing the interplay between fractional vortices, frustration, and topology in stabilizing this exotic SC phase.

cond-mat.supr-con↗

arXiv2024

Emergent Intermediate Phase in the $J_1$-$J_2$ XY model from Tensor Network Approaches

We investigate the finite-temperature phase diagram of the classical $J_1$-$J_2$ XY model on a square lattice using a tensor network approach designed for frustrated spin systems. This model, characterized by competing nearest-neighbor and next-to-nearest-neighbor interactions, exhibits a complex interplay between $U(1)$ and $Z_2$ symmetries. Our study reveals an emergent intermediate phase around $J_2/J_1 \sim 0.505$, which is characterized by a $Z_2$ long-range stripe order without phase coherence in the XY spins. The intermediate phase features two well-separated phase transitions: a higher-temperature Ising transition and a lower-temperature Berezinskii-Kosterlitz-Thouless transition. The relative separation between these transitions is significantly larger than previously reported, enabling a clearer investigation of their distinct thermodynamic properties. For $0.5<J_2/J_1 < 0.501$, two transitions merge into a single first-order phase transition, a phenomenon that cannot be explained solely by mapping to the Ising-XY model. As $J_2/J_1 \to \infty$, the transition evolves continuously into the BKT universality class. These findings advance the understanding of the mechanisms driving phase transitions in frustrated spin systems and suggest potential experimental realizations in platforms such as ultracold atoms, Josephson junction arrays, and optical lattices.

cond-mat.str-el↗

arXiv2024

Theory of charge-6e condensed phase in Kagome lattice superconductors

We develop a Ginzburg-Landau theory for commensurate pair density wave (PDW) states in a hexagonal lattice system, relevant to the kagome superconductors $\rm{AV_3Sb_5}$. Compared to previous theoretical frameworks, the commensurate wave vectors permit additional symmetric terms in the free energy, altering the system's ground state and its degeneracy. In particular, we analyze topological defects in the energetically favorable $\psi_{\text{kagome}}$ ground state and find that kinks on domain walls can carry $1/3$ topological charges. We further establish a correspondence between the SC fluctuations in these states and an effective $J_1-J_2$ frustrated XY model on the emergent kagome lattice. By employing a state-of-the-art numerical tensor network method, we rigorously solve this effective model at finite temperatures and confirm the existence of a vestigial phase characterized by $1/3$ vortex-antivortex pairs in low temperatures with the absence of phase coherence of Cooper pairs, which is dual to the charge-$6e$ condensed phase. Our theory provides a potential explanation for the vestigial charge-$6e$ magnetoresistance oscillations observed in recent experiments [J. Ge, et. al., Phys. Rev. X 14, 021025 (2024)].

cond-mat.str-el↗

arXiv2023

Unified tensor network theory for frustrated classical spin models in two dimensions

Frustration is a ubiquitous phenomenon in many-body physics that influences the nature of the system in a profound way with exotic emergent behavior. Despite its long research history, the analytical or numerical investigations on frustrated spin models remain a formidable challenge due to their extensive ground state degeneracy. In this work, we propose a unified tensor network theory to numerically solve the frustrated classical spin models on various two-dimensional (2D) lattice geometry with high efficiency. We show that the appropriate encoding of emergent degrees of freedom in each local tensor is of crucial importance in the construction of the infinite tensor network representation of the partition function. The frustrations are thus relieved through the effective interactions between emergent local degrees of freedom. Then the partition function is written as a product of a one-dimensional (1D) transfer operator, whose eigen-equation can be solved by the standard algorithm of matrix product states rigorously, and various phase transitions can be accurately determined from the singularities of the entanglement entropy of the 1D quantum correspondence. We demonstrated the power of our unified theory by numerically solving 2D fully frustrated XY spin models on the kagome, square and triangular lattices, giving rise to a variety of thermal phase transitions from infinite-order Brezinskii-Kosterlitz-Thouless transitions, second-order transitions, to first-order phase transitions. Our approach holds the potential application to other types of frustrated classical systems like Heisenberg spin antiferromagnets.

cond-mat.stat-mech↗

arXiv2023

Tensor network approach to the fully frustrated XY model on a kagome lattice with a fractional vortex-antivortex pairing transition

We have developed a tensor network approach to the two-dimensional fully frustrated classical XY spin model on the kagome lattice, and clarified the nature of the possible phase transitions of various topological excitations.We find that the standard tensor network representation for the partition function does not work due to the strong frustrations in the low temperature limit. To avoid the direct truncation of the Boltzmann weight, based on the duality transformation, we introduce a new representation to build the tensor network with local tensors lying on the centers of the elementary triangles of the kagome lattice. Then the partition function is expressed as a product of one-dimensional transfer matrix operators, whose eigen-equation can be solved by the variational uniform matrix product state algorithm accurately. The singularity of the entanglement entropy for the one-dimensional quantum operator provides a stringent criterion for the possible phase transitions. Through a systematic numerical analysis of thermodynamic properties and correlation functions in the thermodynamic limit, we prove that the model exhibits a single Berezinskii-Kosterlitz-Thouless phase transition only, which is driven by the unbinding of $1/3$ fractional vortex-antivortex pairs determined at $T_{c}\simeq 0.075J_{1}$ accurately. The absence of long-range order of chirality or quasi-long range order of integer vortices has been verified in the whole finite temperature range. Thus the long-standing controversy about the phase transitions in this fully frustrated XY model on the kagome lattice is solved rigorously, which provides a plausible way to understand the charge-6e superconducting phase observed experimentally in the two-dimensional kagome superconductors.

cond-mat.str-el↗

arXiv2023

Two-stage melting of an inter-component Potts long-range order in two dimensions

Interplay of topology and competing interactions can induce new phases and phase transitions at finite temperatures. We consider a weakly coupled two-dimensional hexatic-nematic XY model with a relative $Z_3$ Potts degrees of freedom,and apply the matrix product state method to solve this model rigorously. Since the partition function is expressed as a product of two-legged one-dimensional transfer matrix operator, an entanglement entropy of the eigenstate corresponding to the maximal eigenvalue of this transfer operator can be used as a stringent criterion to determine various phase transitions precisely. At low temperatures, the inter-component $Z_3$ Potts long-range order (LRO) exists, indicating that the hexatic and nematic fields are locked together and their respective vortices exhibit quasi-LRO. In the hexatic regime, below the BKT transition of the hexatic vortices, the inter-component $Z_3$ Potts LRO appears, accompanying with the binding of nematic vortices. In the nematic regime, however, the inter-component $Z_3$ Potts LRO undergoes a two-stage melting process. An intermediate Potts liquid phase emerges between the Potts ordered and disordered phases, characterized by an algebraic correlation with formation of charge-neutral pairs of both hexatic and nematic vortices. These two-stage phase transitions are associated with the proliferation of the domain walls and vortices of the relative $Z_3$ Potts variable, respectively. Our results thus provide a prototype example of two-stage melting of a two-dimensional long-range order, driven by multiple topological defects.

cond-mat.stat-mech↗

arXiv2022

Tensor network approach to the two-dimensional fully frustrated XY model and a chiral ordered phase

A general framework is proposed to solve the two-dimensional fully frustrated XY model for the Josephson junction arrays in a perpendicular magnetic field. The essential idea is to encode the ground-state local rules induced by frustrations in the local tensors of the partition function. The partition function is then expressed in terms of a product of one-dimensional transfer matrix operator, whose eigen-equation can be solved by an algorithm of matrix product states rigorously. The singularity of the entanglement entropy for the one-dimensional quantum analogue provides a stringent criterion to distinguish various phase transitions without identifying any order parameter a prior. Two very close phase transitions are determined at $T_{c1}\approx 0.4459$ and $T_{c2}\approx 0.4532$, respectively. The former corresponding to a Berezinskii-Kosterlitz-Thouless phase transition describing the phase coherence of XY spins, and the latter is an Ising-like continuous phase transition below which a chirality order with spontaneously broken $Z_2$ symmetry is established.

cond-mat.str-el↗

arXiv2022

Phase coherence of pairs of Cooper pairs as quasi-long-range order of half-vortex pairs in a two-dimensional bilayer system

It is known that the loss of phase coherence of Cooper pairs in two-dimensional (2D) superconductivity corresponds to the unbinding of vortex-antivortex pairs with the quasi-long-range order (quasi-LRO) in the order-parameter phase field, described by the Berezinskii-Kosterlizt-Thouless (BKT) transition of a 2D XY model. Here we show that the second-order Josephson coupling can induce an exotic superconducting phase in a bilayer system. By using tensor-network methods, the partition function of the 2D classical model is expressed as a product of 1D quantum transfer operator, whose eigen-equation can be solved by an algorithm of matrix product states rigorously. From the singularity shown by the entanglement entropy of the 1D quantum analogue, various phase transitions can be accurately determined. Below the BKT phase transition, an inter-layer Ising long-range order is established at $T_{Ising}$, and the phase coherence of both intra-layers and inter-layers is locked together. For two identical layers, the Ising transition coincides with the BKT transition at a multi-critical point. For two inequivalent layers, however, there emerges an intermediate quasi-LRO phase ($T_{Ising}<T<T_{BKT}$), where the vortex-antivortex bindings occur in the layer with the larger intra-layer coupling, but only half-vortex pairs with topological strings exist in the other layer, corresponding to the phase coherence of pairs of Cooper pairs. So our study provides a promising way to realize the charge-4e superconductivity in a bilayer system.

cond-mat.stat-mech↗

arXiv2021

Hybrid Berezinskii-Kosterlitz-Thouless and Ising topological phase transition in the generalized two-dimensional XY model using tensor networks

In tensor network representation, the partition function of a generalized two-dimensional XY spin model with topological integer and half-integer vortex excitations is mapped to a tensor product of one-dimensional quantum transfer operator, whose eigen-equation can be solved by an algorithm of variational uniform matrix product states. Using the singularities of the entanglement entropy, we accurately determine the complete phase diagram of this model. Both the integer vortex-antivortex binding and half-integer vortex-antivortex binding phases are separated from the disordered phase by the usual Berezinskii-Kosterlitz-Thouless (BKT) transitions, while a continuous topological phase transition exists between two different vortex binding phases, exhibiting a logarithmic divergence of the specific heat and exponential divergence of the spin correlation length. A new hybrid BKT and Ising universality class of topological phase transition is thus established. We further prove that three phase transition lines meets at a multi-critical point, from which a deconfinement crossover line extends into the disordered phase.

cond-mat.str-el↗