arXiv subjects

Yi-Cai Zhang

Publications and source records attributed to Yi-Cai Zhang.

At least 19 recordsLinked to original sources

arXiv2026

Measure-zero delocalization in the complex plane: exact mobility arcs in a non-Hermitian off-diagonal quasiperiodic lattice

We investigate Anderson localization in a one-dimensional lattice with non-Hermitian off-diagonal quasiperiodic disorder, extending a recently studied Hermitian mosaic model to the non-Hermitian regime. Using Avila's global theory, we derive the exact Lyapunov exponent and the complete phase diagram in the complex energy plane. This work contains two central findings. First, we discover mobility arcs---open curved segments in the complex plane---as a new class of mobility edges and the generic form of open mobility edges, which coexist with closed mobility rings in a complementary parameter regime. These arcs share the same localization physics as the previously reported mobility lines: eigenstates are delocalized if and only if their energies lie exactly on these sets; any deviation yields localized states. This constitutes a striking measure-zero delocalization phenomenon: delocalized states occupy only zero-measure sets (arcs or lines) in the complex plane, in sharp contrast to the mobility rings, which enclose a finite-area region of delocalized states. Second, we reveal that mobility rings, arcs, and lines all share a common mathematical origin in the generalized Joukowski transformation $P(E) = \frac{1}{2}(u - w^2/u)$, rooted in the algebraic structure of the underlying polynomial: the preimage of the boundary of an elliptical region under the polynomial map $P(E)$ gives the rings, while the branch cut inside this ellipse gives rise to the mobility arcs and lines in the complementary parameter regime.

cond-mat.dis-nn↗

arXiv2025

Multifractal-enriched mobility edges and emergent quantum phases in Rydberg atomic arrays

Anderson localization describes disorder-induced phase transitions, distinguishing between localized and extended states. In quasiperiodic systems, a third multifractal state emerges, characterized by unique energy and wave functions. However, the corresponding multifractal-enriched mobility edges and three-state-coexisting quantum phases have yet to be experimentally detected. In this work, we propose exactly-solvable one-dimensional quasiperiodic lattice models that simultaneously host three-state-coexisting quantum phases, with their phase boundaries analytically derived via Avila's global theorem. Furthermore, we propose experimental protocols via Rydberg atom arrays to realize these states. Notably, we demonstrate a spectroscopic technique capable of measuring inverse participation ratios across real-space and dual-space domains, enabling simultaneous characterization of localized, extended, and multifractal quantum phases in systems with up to tens of qubits. Our work opens new avenues for the experimental exploration of Anderson localization and multifractal states in artificial quantum systems.

cond-mat.dis-nn↗

arXiv2025

The odd-even effect of mosaic modulation period of quasi-periodic hopping on the Anderson localization in a one-dimensional lattice model

In this study, we investigate Anderson localization in a one-dimensional lattice with a mosaic off-diagonal quasiperiodic hopping. Our findings reveal that the localization behavior of zero-energy states is highly dependent on the parity of the mosaic modulation period, denoted as $κ$. Specifically, when $κ$ is an odd integer, there is no Anderson localization transition even for large quasiperiodic hopping strengths, and the zero-energy state remains in a critical state. On the other hand, for an even $κ$ and a generic quasiperiodic hopping, the zero-energy state becomes a localized edge state at either the left or right end of the system. Additionally, we observe that the geometric mean value of the energy spectrum is equal to the constant hopping for an even $κ$, while for an odd $κ$, it is equal to the geometric mean value of the hopping. This odd-even effect of the mosaic period also extends to other eigenstates near zero energy. More specifically, for an odd $κ$, there exists an energy window in which the eigenstates remain critical even for strong quasiperiodic hopping. In contrast, for an even $κ$, an Anderson localization transition occurs as the hopping strength increases. Furthermore, we are able to accurately determine the Lyapunov exponent $γ(E)$ and the mobility edges $E_c$. By analyzing the Lyapunov exponent, we identify critical regions in the hopping-energy parameter planes. Additionally, as the energy approaches the mobility edges, we observe a critical index of localization length of $ν=1$. Finally, we demonstrate that different systems can be characterized by their Lyapunov exponent $γ(E)$ and Avila's acceleration $ω(E)$.

cond-mat.dis-nn↗

arXiv2025

A steady solution to the hydrodynamic equation and incommensurate magnetization in a U(2) invariant superfluid

At the zero temperature limit, a one-dimensional steady solution to the hydrodynamic equation of a U(2) invariant superfluid is obtained. This solution reveals that the magnitude of magnetization is always directly proportional to the particle number density. Furthermore, the problem can be interpreted as a particle's motion in a central force field. It is demonstrated that the particle's orbits are elliptical in shape, with a precession angle determined by a non-zero mass current. This suggests that the spatial periods of the three component magnetizations are not commensurate. These findings indicate that the coupling of mass superflow and magnetization distortions usually results in an incommensurate magnetization.

cond-mat.quant-gas↗

arXiv2025

Double commutator method for a two band Bose-Einstein condensate: superfluid density of a flat band superfluid

In this work, we propose a double commutator method for a general two-band bosonic superfluid. First and foremost, we prove that the sum of the superfluid and normal densities is equal to the weight of the f-sum rule. This weight can be easily determined by analyzing the ground state wave function. Once we have determined the excitation gap of the upper band, we can calculate the normal density by evaluating the average value of a double commutator between the velocity operator and the Hamiltonian. As an application of this method, we investigate the superfluid density of a flat band Bose-Einstein condensate (BEC). Using the Bogoliubov method, we calculate the sound velocity and excitation gap, which allows us to obtain the normal and superfluid densities explicitly. Our findings indicate that the superfluid density is directly proportional to the product of the square of the sound velocity and the compressibility. Furthermore, the existence of a non-vanishing superfluid density depends on the form of the interaction. For example, in the case of U(2) invariant interactions, the superfluid density is zero. Additionally, we have observed that for small interactions, the superfluid density is directly proportional to the product of the interaction parameter and the quantum metric. The double commutator method indicates that the correction of the excitation gap by interactions is the origin of the non-vanishing superfluid density of a flat band BEC. Up to the linear order of the interaction parameters, all the results for the excitation gap, the normal and superfluid densities in a flat band BEC can also be obtained through a simple perturbation theory. Our work provides another unique perspective on the superfluid behavior of a flat band BEC.

cond-mat.quant-gas↗

arXiv2025

Exact mobility line and mobility ring in the complex energy plane of a flat band lattice with a non-Hermitian quasiperiodic potential

In this study, we investigate the problem of Anderson localization in a one-dimensional flat band lattice with a non-Hermitian quasiperiodic on-site potential. First of all, we discuss the influences of non-Hermitian potentials on the existence of critical states. Our findings show that, unlike in Hermitian cases, the non-Hermiticity of the potential leads to the disappearance of critical states and critical regions. Furthermore, we are able to accurately determine the Lyapunov exponents and the mobility edges. Our results reveal that the mobility edges form mobility lines and mobility rings in the complex energy plane. Within the mobility rings, the eigenstates are extended, while the localized states are located outside the mobility rings. For mobility line cases, only when the eigenenergies lie on the mobility lines, their corresponding eigenstates are extended states.Finally, as the energy approaches the mobility edges, we observe that, differently from Hermitian cases, here the critical index of the localization length is not a constant, but rather varies depending on the positions of the mobility edges.

cond-mat.dis-nn↗

arXiv2024

Hydrodynamic equations for a U(N) invariant superfluid

In this paper, we develop the appropriate set of hydrodynamic equations in a U(N) invariant superfluid that couple the dynamics of superflow and magnetization. In the special case when both the superfluid and normal velocities are zero, the hydrodynamic equations reduce to a generalized version of Landau-Lifshitz equation for ferromagnetism with U(N) symmetry. When both velocities are non-zero, there appears couplings between the superflow and magnetization dynamics, and the superfluid velocity no longer satisfies the irrotational condition. On the other hand, the magnitude of magnetization is no longer a constant of motion as was the case for the standard Landau-Lifshitz theory. In comparison with the simple superfluid, the first sound and second sounds are modified by a non-zero magnetization through various thermodynamic functions. For U(2) invariant superfluid, we get both (zero-) sound wave and a spin wave at zero temperature. It is found that the dispersion of spin wave is always quadratic, which is consistent with detailed microscopic analysis. In the Appendix, we show that the hydrodynamic equation for a U(N) invariant superfluid can be obtained from the general hydrodynamic equation with arbitrary internal symmetries.

cond-mat.quant-gas↗

arXiv2023

Energy bands in a three dimension simple cubic lattice of contact potential

In this work, we investigate energy bands in a three dimensional simple cubic lattice of contact potential. The energy bands in the first Brillouin Zone are obtained with Ewald's summation method. In comparison with single point potential, the presence of lattice potential changes the existence condition of negative energy states near zero energy. It is found that the system always has negative energy states for an arbitrarily weak periodic potential. In addition, we prove that if an irreducible unitary representation is not a trivial representation of group of wave vector, the corresponding wave functions at lattice sites would be zero. With this theorem, the degeneracy of energy bands is explained with group theory. Furthermore, we find that there exists some energy bands which are not affected by the lattice potential. We call their corresponding eigenstates as dark states. The physical mechanism of the dark states is explained by explicitly constructing the standing wave-type Bloch wave functions.

cond-mat.quant-gas↗

arXiv2023

Quantum Transports in Two-Dimensions with Long Range Hopping: Shielding, Localization and the Extended Isolated State

We investigate the effects of disorder and shielding on quantum transports in a two dimensional system with all-to-all long range hopping. In the weak disorder, cooperative shielding manifests itself as perfect conducting channels identical to those of the short range model, as if the long range hopping does not exist. With increasing disorder, the average and fluctuation of conductance are larger than those in the short range model, since the shielding is effectively broken and therefore long range hopping starts to take effect. Over several orders of disorder strength (until $\sim 10^4$ times of nearest hopping), although the wavefunctions are not fully extended, they are also robustly prevented from being completely localized into a single site. Each wavefunction has several localization centers around the whole sample, thus leading to a fractal dimension remarkably smaller than 2 and also remarkably larger than 0, exhibiting a hybrid feature of localization and delocalization. The size scaling shows that for sufficiently large size and disorder strength, the conductance tends to saturate to a fixed value with the scaling function $β\sim 0$, which is also a marginal phase between the typical metal ($β>0$) and insulating phase ($β<0$). The all-to-all coupling expels one isolated but extended state far out of the band, whose transport is extremely robust against disorder due to absence of backscattering. The bond current picture of this isolated state shows a quantum version of short circuit through long hopping.

cond-mat.dis-nn↗

arXiv2023

Numerical Investigation of Localization in Two-Dimensional Quasiperiodic Mosaic Lattice

A one-dimensional lattice model with mosaic quasiperiodic potential is found to exhibit interesting localization properties, e.g., clear mobility edges [Y. Wang et al., Phys. Rev. Lett. \textbf{125}, 196604 (2020)]. We generalize this mosaic quasiperiodic model to a two-dimensional version, and numerically investigate its localization properties: the phase diagram from the fractal dimension of the wavefunction, the statistical and scaling properties of the conductance. Compared with disordered systems, our model shares many common features but also exhibits some different characteristics in the same dimensionality and the same universality class. For example, the sharp peak at $g\sim 0$ of the critical distribution and the large $g$ limit of the universal scaling function $β$ resemble those behaviors of three-dimensional disordered systems.

cond-mat.mes-hall↗

arXiv2022

Infinite bound states and hydrogen atom-like energy spectrum induced by a flat band

In this work, we investigate the bound state problem in one dimensional spin-1 Dirac Hamiltonian with a flat band. It is found that, the flat band has significant effects on the bound states. For example, for Dirac delta potential $gδ(x)$, there exists one bound state for both positive and negative potential strength $g$. Furthermore, when the potential is weak, the bound state energy is proportional to the potential strength $g$. For square well potential, the flat band results in the existence of infinite bound states for arbitrarily weak potential. In addition, when the bound state energy is very near the flat band, the energy displays hydrogen atom-like spectrum, i.e., the bound state energies are inversely proportional to the square of natural number $n$ (e.g., $E_n\propto 1/n^2, n=1,2,3,...$). Most of the above nontrivial behaviors can be attributed to the infinitely large density of states of flat band and its ensuing $1/z$ singularity of Green function. The combination of a short-ranged potential and flat band provides a new possibility to get infinite number of bound states and hydrogen atom-like energy spectrum. In addition, our findings would provide some useful insights in the understanding of many-body physics of flat band.

quant-ph↗

arXiv2022

Infinite bound states and $1/n$ energy spectrum induced by a Coulomb-like potential of type III in a flat band system

In this work, we investigate the bound states in a one-dimensional spin-1 flat band system with a Coulomb-like potential of type III, which has a unique non-vanishing matrix element in basis $|1\rangle$. It is found that, for such a kind of potential, there exists infinite bound states. Near the threshold of continuous spectrum, the bound state energy is consistent with the ordinary hydrogen-like atom energy level formula with Rydberg correction. In addition, the flat band has significant effects on the bound states. For example, there are infinite bound states which are generated from the flat band. Furthermore, when the potential is weak, the bound state energy is proportional to the Coulomb-like potential strength $α$. When the bound state energies are very near the flat band, they are inversely proportional to the natural number $n$ (e.g., $E_n\propto 1/n, n=1,2,3,...$). Further we find that the energy spectrum can be well described by quasi-classical approximation (WKB method). Finally, we give a critical potential strength $α_c$ at which the bound state energy reaches the threshold of continuous spectrum. \textbf{After crossing the threshold, the bound states in the continuum (BIC) may exist in such a flat band system.

quant-ph↗

arXiv2022

Proposed realization of critical regions in a one-dimensional flat band lattice with a quasi-periodic potential

In the previous work, the concept of critical region in a generalized Aubry-André model (Ganeshan-Pixley-Das Sarma's model) has been set up. In this work we propose that the critical region can be realized in a one-dimensional flat band lattice system with a quasi-periodic potential. It is found that the above flat band lattice model can be reduced into an effective Ganeshan-Pixley-Das Sarma's model where the effective parameter $α=V_0/(2E)$ with potential strength $V_0$ and eigenenergy $E$. It is shown that there are very rich physics in this model. Depending on $|α|<1$ or $|α|\geq1$, the effective quasi-periodic potential would be bounded or unbounded. For these two cases, the Lyapunov exponent [$γ(E)$], mobility edges ($E_c$) and critical indices ($ν$) of localized length are obtained exactly. In addition, several localized state regions, extended state regions and critical regions would appear in the parameter $V_0-E$ plane. For a given potential strength $V_0$, the localized-extended and localized-critical transitions can co-exist. Furthermore, we find the critical index of localized length $ξ(E)=1/γ(E)$ is $ν=1$ near localized-extended transitions and $ν=1/2$ near the localized-critical transitions. Near the transition point between the bound ($|α|<1$) and unbounded ($|α|\geq1$) cases, i.e, $|α|=|V_0/(2E)|= 1$, the derivative of Lypunov exponent of localized states with respect to energy is discontinuous. The localized states in bounded and unbounded cases can be distinguished from each other by Avila's acceleration. At the end, we find that near the transition point, there also exist critical-extended transitions in the phase diagram.

cond-mat.dis-nn↗

arXiv2022

Lyapunov exponent, mobility edges, and critical region in the generalized Aubry-Andre model with an unbounded quasiperiodic potential

In this work, we investigate the Anderson localization problems of the generalized Aubry-André model (Ganeshan-Pixley-Das Sarma's model) with an unbounded quasi-periodic potential where the parameter $|α|\geq1$. The Lyapunov exponent $γ(E)$ and the mobility edges $E_c$ are exactly obtained for the unbounded quasi-periodic potential. With the Lyapunov exponent, we find that there exists a critical region in the parameter $λ-E$ plane. The critical region consists of critical states. In comparison with localized and extended states, the fluctuation of spatial extensions of the critical states is much larger. The numerical results show that the scaling exponent of inverse participation ratio (IPR) of critical states $x\simeq0.5$. Furthermore, it is found that the critical indices of localized length $ν=1$ for bounded ($|α|<1$) case and $ν=1/2$ for unbounded ($|α|\geq1$) case. The above distinct critical indices can be used to distinguish the localized-extended from localized-critical transitions. At the end, we show that the systems with different $E$ for both cases of $|α|<1$ and $|α|\geq1$ can be classified by the Lyapunov exponent $γ(E)$ and Avila's quantized acceleration $ω(E)$.

cond-mat.dis-nn↗

arXiv2022

Superfluid density and collective modes of fermion superfluid in dice lattice

The superfluid properties of attractive Hubbard model in dice lattice are investigated. It is found that three superfluid order parameters increase as the interaction increases. When the filling factor falls into the flat band, due to the infinite large density of states, the resultant superfluid order parameters are proportional to interaction strength, which is in striking contrast with the exponentially small counterparts in usual superfluid (or superconductor). When the interaction is weak, and the filling factor is near the bottom of the lowest band (or the top of highest band), the superfluid density is determined by the effective mass of the lowest (or highest) single-particle band. When the interaction is strong and filling factor is small, the superfluid density is inversely proportional to interaction strength, which is related to effective mass of tightly bound pairs. In the strong interaction limit and finite filling, the asymptotic behaviors of superfluid density can be captured by a parabolic function of filling factor. Furthermore, when the filling is in flat band, the superfluid density shows a logarithmic singularity as the interaction approaches zero. In addition, there exist three undamped collective modes for strong interactions. The lowest excitation is gapless phonon, which is characterized by the total density oscillations. The two others are gapped Leggett modes, which correspond relative density fluctuations between sublattices. The collective modes are also reflected in the two-particle spectral functions by sharp peaks. Furthermore, it is found that the two-particle spectral functions satisfy an exact sum-rule, which is directly related to the filling factor (or density of particle). The sum-rule of the spectral functions may be useful to distinguish between the hole-doped and particle-doped superfluid (superconductor) in experiments.

cond-mat.quant-gas↗

arXiv2022

Bound states in the continuum (BIC) protected by self-sustained potential barriers in a flat band system

In this work, we investigate the bound states in the continuum (BIC) of a one-dimensional spin-1 flat band system. It is found that, when the potential is sufficiently strong, there exists an effective attractive potential well surrounded by infinitely high self-sustained barriers. Consequently, there exist some BIC in the effective potential well. These bound states are protected by the infinitely high potential barriers, which could not decay into the continuum.} Taking a long-ranged Coulomb potential and a short-ranged exponential potential as two examples, the bound state energies are obtained. For a Coulomb potential, there exists a series of critical potential strengths, near which the bound state energy can go to infinity. For a sufficiently strong exponential potential, there exists two different bound states with a same number of wave function nodes. The existence of BIC protected by the self-sustained potential barriers is quite a universal phenomenon in the flat band system under a strong potential. A necessary condition for the existence of BIC is that the maximum value of potential is larger than two times band gap.

cond-mat.quant-gas↗

arXiv2020

Superfluid density, Josephson relation and pairing fluctuations in a multi-component fermion superfluid

In this work, a Josephson relation is generalized to a multi-component fermion superfluid. Superfluid density is expressed through a two-particle Green function for pairing channels. When the system has only one gapless collective excitation mode, the Josephson relation is simplified, which is given in terms of the order parameters and the trace of two-particle Green functions. In the presence of inversion symmetry, the superfluid density is directly related to the inverse of pairing fluctuation matrix. The results of the superfluid density in Haldane model show that the generalized Josephson relation can be also applied into a multi-band fermion superfluid in lattice.

cond-mat.supr-con↗

arXiv2020

Normal density and moment of inertia of a moving superfluid

In this work, the normal density $ρ_n$ and moment of inertia of a moving superfluid are investigated. We find that, even at zero temperature, there exists a finite normal density for the moving superfluid. When the velocity of superfluid reaches sound velocity, the normal density becomes total mass density $ρ$, which indicates that the system losses superfluidity. At the same time, the Landau's critical velocity also becomes zero. The existence of the non-zero normal density is attributed to the coupling between the motion of superflow and density fluctuation in transverse directions. With Josephson relation, the superfluid density $ρ_s$ is also calculated and the identity $ρ_s+ρ_n=ρ$ holds. Further more, we find that the finite normal density also results in a quantized moment of inertia in a moving superfluid trapped by a ring. The normal density and moment of inertia at zero temperature could be verified experimentally by measuring the angular momentum of a moving superfluid in a ring trap.

cond-mat.quant-gas↗