Two-leg Ladder Research Articles

Metal to Wigner-Mott insulator transition in two-leg ladders

We study theoretically the quantum phase transition from a metal to a Wigner-Mott insulator at fractional commensurate filling on a two-leg ladder. We show that a continuous transition out of a symmetry-preserving Luttinger liquid metal is possible where the onset of insulating behavior is accompanied by the breaking of the lattice translation symmetry. At fillings $\nu = 1/m$ per spin per unit cell, we find that the spin degrees of freedom also acquire a gap at the Wigner-Mott transition for odd integer $m$. In contrast for even integer $m$, the spin sector remains gapless and the resulting insulator is a ladder analog of the two-dimensional spinon surface state. In both cases, a charge neutral spinless mode remains gapless across the Wigner-Mott transition. We discuss physical properties of these transitions, and comment on insights obtained for thinking about continuous Wigner-Mott transitions in two-dimensional systems which are being studied in moire materials.

Hydrated polymorphs of 2,3,4,5,6-pentachlorobenzoic acid: Crystallographical and computational analyses of disordered hydrogen-bonding networks

The title compound, 2,3,4,5,6-pentachlorobenzoic acid (PCBAH), was found to have two crystal polymorphs, I and II. In this work, novel two hydrated polymorphs, polymorph III and IV, were reported. An asymmetric unit of the polymorph III is comprised of one PCBAH and a water molecule. They align alternatively along the a axis, forming C22(6) hydrogen-bonding. The water molecule makes another hydrogen bond with a water molecule in an inversion symmetry to give two-legged ladder hydrogen-bonding network. In polymorph IV, there are two PCBAHs, 2,3,4,5,6-pentachlorobenzate (PCBA) and H3O+ in an asymmetric unit. H3O+ molecule makes hydrogen-bonding with two PCBA anions, forming C22(6) hydrogen-bonding along the 21 axis. Two PCBAH molecule make hydrogen bonds with both H3O+ and PCBA. In both hydrated polymorphs, hydrogen atoms of water molecules are disordered. The positions of hydrogen atoms of the water molecules were determined with assistance of computational calculations under the crystalline environment.

Flux-controlled skin effect and topological transition in a dissipative two-leg ladder model

The synthetic gauge field and dissipation are of crucial importance in both fundamental physics and applications. Here, we investigate the interplay of the uniform flux and the on-site gain and loss by considering a dissipative two-leg ladder model. By calculating the spectral winding number and the generalized Brillouin zone, we predict the non-Hermitian skin effect, whose skin modes display the bipolar localization. This skin effect emerges when the flux is not an integer multiple of $\ensuremath{\pi}$. We further demonstrate the breakdown of the chiral currents due to the presence of the skin effect by studying single-particle dynamics. Moreover, we show that the non-Hermiticity can drive a flux-dependent topological transition characterized by a hidden Chern number. Our results provide a scheme to manipulate the non-Hermitian skin effect and topological phase transitions, which may find potential applications in lasing, light manipulating, and signal processing.

Theoretical study of the magnetic properties of the CoCu2O3 compound

In this paper we present a theoretical study of the magnetic properties of the ${\mathrm{CoCu}}_{2}{\mathrm{O}}_{3}$ compound. The magnetic effective exchange interactions and zeroth-field splitting were computed using ab initio methods, then the magnetic order and transition temperature were determined using classical Monte Carlo simulations. We showed that, unlike other members of the $A{\mathrm{Cu}}_{2}{\mathrm{O}}_{3}$ family, the presence of an additional magnetic atom, associated with a large folding of the puckered layers in the ($\stackrel{P\vec}{a}, \stackrel{P\vec}{b}$) directions, induces a magnetic pattern based on coupled three-leg ladders, quite different from the two-leg structural ladders. The propagation vector has been found to be $\stackrel{P\vec}{q}=(0,\frac{1}{2},\frac{1}{2})$. It is associated with a doubly degenerated ground state suggesting a doubling of the unit cell. The large ${\mathrm{Co}}^{2+}$-ion anisotropy was shown to be of crucial importance in the high transition temperature observed in this compound.

Controlling localized states in a two-leg ladder lattice with diagonal edges via gain/loss [Invited

Gain and loss engineering can bring fascinating physical phenomena and lead to useful potential applications in optics and photonics. Here we study a two-leg ladder lattice with diagonal-edge open boundary condition which supports zero-energy modes with localization phenomena. By considering the on-site gain and loss on two legs respectively, we see the phase transition of features from localization at edges to extension into bulk. Meanwhile, the effective magnetic flux can further enhance the localization effect. Simulations are performed to verify the manipulation of localization via gain and loss in our model. This work offers the opportunity for controlling the localized states in a finite system through the non-Hermiticity and shows potential application towards implementing high-power laser arrays in both real space and synthetic dimensions.

Thermodynamic signature of topological quantum phase transition in a two-leg Kitaev ladder

We study the topological quantum phase transitions (QPTs) and quantum criticality of a two-leg Kitaev ladder. In the absence of superconducting phase difference, the thermal Drude weight portrays well the gapped topological quantum phases (Dth=0) and gapless quantum criticality (Dth>0), which is further manifested by the critical energy spectrum with different gapless linear relation modes. The self-dual quantum criticality is demonstrated by the Grüneisen ratio (GR) Γ= constant irrelevant of temperature. Tuning the superconducting phase difference Φ=π, the system undergoes a gapped topological nontrivial phase transition into a gapless trivial one, manifested by the quadratic contact point at the center of Brillouin zone. Meanwhile, it is identified by the temperature dependent power-law divergence: Γ∼±T−1 at low temperature, which is similar to the general QPT. In particular, with the chemical potential vanishing, one can obtain full flat bands, giving rise to the discontinuous topological QPT. Furthermore, it is worth noting that the scaling of GR provides a new thermodynamic means to check the order of topological QPTs, which falls on a universal curve or not, indicating the continuous or discontinuous transition.

Quantum criticality in interacting bosonic Kitaev-Hubbard models

Motivated by recent work on the non-Hermitian skin effect in the bosonic Kitaev-Majorana model, we study the quantum criticality of interacting bosonic Kitaev-Hubbard models on a chain and a two-leg ladder. In the hard-core limit, we show exactly that the non-Hermitian skin effect disappears via a transformation from hard-core bosonic models to spin-1/2 models. We also show that hard-core bosons can engineer the Kitaev interaction, the Dzyaloshinskii-Moriya interaction and the compass interaction in the presence of the complex hopping and pairing terms. Importantly, quantum criticalities of the chain with a three-body constraint and unconstrained soft-core bosons are investigated by the density matrix renormalization group method. This work reveals the effect of many-body interactions on the non-Hermitian skin effect and highlights the power of bosons with pairing terms as a probe for the engineering of interesting models and quantum phase transitions.

Root- N Krylov-space correction vectors for spectral functions with the density matrix renormalization group

We propose a method to compute spectral functions of generic Hamiltonians using the density matrix renormalization group (DMRG) algorithm directly in the frequency domain, based on a modified Krylov space decomposition to compute the correction-vectors. Our approach entails the calculation of the root-N (N=2 is the standard square root) of the Hamiltonian propagator using Krylov space decomposition, and repeating this procedure N times to obtain the actual correction-vector. We show that our method greatly alleviates the burden of keeping a large bond dimension at large target frequencies, a problem found with conventional correction-vector DMRG, while achieving better computational performance at large N. We apply our method to spin and charge spectral functions of t-J and Hubbard models in the challenging two-leg ladder geometry, and provide evidence that the root-N approach reaches a much improved resolution compared to conventional correction-vector.

Nonlinear Bloch dynamics and spin-wave generation in a Bose-Hubbard ladder subject to effective magnetic field.

The two-leg magnetic ladder is the simplest and ideal model to reflect the coupling effects of lattice and magnetic field. It is of great significance to study some novel phases, topological characteristics, and chiral characteristics in condensed matter physics. In particular, the left-right leg degree of freedom can be regarded as a pseudospin, and the two-leg magnetic ladder also provides an ideal platform for the study of spin dynamics. Here the ground state, Bloch oscillations (BOs), and spin dynamics of the interacting two-leg magnetic ladder subject to an external linear force are studied by using variational approach and numerical simulation. In the absence of the external linear force, the critical condition of transition between the zero-momentum state and plane-wave state is obtained analytically, and the physical mechanism of the ground-state transition is revealed. When the external linear force presents, the occurrence of BOs excites the spin dynamics, and we reveal the chiral BOs and the accompanied spin dynamics of the system in different ground states. In particular, we further study the influence of periodically modulated linear force on BOs and spin dynamics. The frequencies of the linear force corresponding to the resonances and pseudoresonances are obtained analytically, which result in rich nonlinear dynamics. In resonances, stable and strong BOs (with larger amplitude) are observed. In pseudoresonances, because the pseudoresonance frequencies are related to the initial momentum and phase of the wave packet, a dispersion effect takes place and strong diffusion of wave packet occurs. When the frequency is nonresonant, drift and weak dispersion of wave packet occur simultaneously with the wave-packet oscillation. In all cases, the wave-packet dynamics is accompanied with periodic but anharmonic pseudospin oscillation. The BOs and spin dynamics are effectively controlled by periodically modulating the linear force.

Phase diagram of Rydberg-dressed atoms on two-leg triangular ladders

Dressed Rydberg atoms in optical lattices are a promising platform for the quantum simulation of intriguing phenomena emerging in strongly interacting systems. Relevant to such a setup, we investigate the phase diagram of hard-core bosons in a triangular ladder with next-to-nearest-neighbor interaction along each leg and nearest-neighbors interactions without hopping between the legs. For weak interactions, Abelian bosonization predicts a spin density wave and a fully gapless Luttinger liquid phase. Such liquids transition to a 'spin-locked' cluster Luttinger liquid at strong interactions along each leg, as predicted by cluster bosonization. Interestingly, the competition with the zigzag interaction generates a charge density wave, a 'polarized holonic' phase, and a crystalline phase at the filling 2/5, that we address via semi-classical perturbative approach. Exact diagonalization and density matrix renormalization group simulations confirm the predictions and further characterize the phases and their transitions.

Symmetric projected entangled-pair states analysis of a phase transition in coupled spin- 12 ladders

Infinite projected entangled-pair states (iPEPS) have been introduced to accurately describe many-body wave functions on two-dimensional lattices. In this context, two aspects are crucial: the systematic improvement of the {\it Ansatz} by the optimization of its building blocks, i.e., tensors characterized by bond dimension $D$, and the extrapolation scheme to reach the "thermodynamic" limit $D \to \infty$. Recent advances in variational optimization and scaling based on correlation lengths demonstrated the ability of iPEPS to capture the spontaneous breaking of a continuous symmetry in phases such as the antiferromagnetic (N\'eel) phase with high fidelity, in addition to valence-bond solids which are already well described by finite-$D$ iPEPS. In contrast, systems in the vicinity of continuous quantum phase transitions still present a challenge for iPEPS, especially when non-abelian symmetries are involved. Here, we consider the iPEPS Ansatz to describe the continuous transition between the (gapless) antiferromagnet and the (gapped) paramagnet that exists in the $S=1/2$ Heisenberg model on coupled two-leg ladders. In particular, we show how accurate iPEPS results can be obtained down to a narrow interval around criticality and analyze the scaling of the order parameter in the N\'eel phase in a spatially anisotropic situation.

Weak ergodicity breaking in Josephson-junction arrays

We study the quantum dynamics of Josephson-junction arrays. We find isolated groups of low-entanglement eigenstates that persist even when the Josephson interaction is strong enough to destroy the overall organization of the spectrum in multiplets, and a perturbative description is no longer possible. These eigenstates lie in the inner part of the spectrum, far from the spectral edge, and provide a weak ergodicity breaking, reminiscent of the quantum scars. Due to the presence of these eigenstates, initializing with a charge-density-wave state, the system does not thermalize and the charge-density-wave order persists for long times. Considering global ergodicity probes, we find that the system tends toward more ergodicity for increasing system size: The parameter range where the bulk of the eigenstates look nonergodic shrinks for increasing system size. We study two geometries, a one-dimensional chain and a two-leg ladder. In the latter case, adding a magnetic flux makes the system more ergodic.

Effect of hopping anisotropy on the d-wave pairing in the Hubbard model: From two-leg ladder to square lattice

In the ladder-type cuprates, superconductivity is argued to be enhanced by increasing the electron hopping in the rung direction, while such an enhancement is not expected in the layered cuprates. Utilizing the quantum Monte Carlo calculations of the Hubbard model, we study the effect of the hopping anisotropy on the d-wave pairing, on the two-leg ladder, the square lattice and the coupled two-leg ladder lattice. On the square lattice, the hopping anisotropy monotonically suppresses the d-wave pairing; while on the two-leg ladder, an optimal hopping anisotropy for the d-wave pairing exists at tx/ty≈0.6. For the coupled two-leg ladder lattice, as the coupling strength ty′/ty decreases, the evolution of the d-wave pairing as a function of the hopping anisotropy behaves as a crossover from the square lattice to the two-leg ladder. Our results provide numerical proof for the possible enhancement of superconductivity in both the ladder-type and layered cuprates.

Pair-density-wave superconductor from doping Haldane chain and rung-singlet ladder

We report the numerical discovery of a pair-density-wave (PDW) superconductor from doping either (i) a spin-one Haldane chain or (ii) a two-leg ladder in the rung singlet phase in which the doped charges occupy a single leg. We model these systems using a generalized Kondo model. The itinerant electrons are correlated and described by the $t-J$ model, and are further coupled to a spin $1/2$ Heisenberg model through the Kondo coupling $J_K$. When the density of electrons $x$ is one, the Mott insulator is in a Haldane phase or in a rung singlet phase depending on whether $J_K$ is negative or positive. Upon doping, a pair-density-wave with $\mathbf Q=\pi$ can emerge for both signs of $J_K$. In the $J_K \rightarrow -\infty$ limit, the model reduces to the recently proposed type II t-J model and we observes a continuous transition between the PDW superconductor and an unconventional Luttinger liquid phase with doping. We also identify a composite order parameter for the superconductor, which can be understood as a Cooper pair formed by two nearby fermionic spin-polarons. Our model and the predicted PDW phase can be experimentally realized by doping S=1 chains formed by Ni$^{2+}$ in a solid state system or a two-leg ladder of fermionic cold atoms with a potential bias between legs, which preferentially dopes carriers into a single leg.

Metastable magnetization plateaus in the S =1 organic spin ladder BIP-TENO induced by a microsecond-pulsed megagauss field

The entire magnetization process in the two-leg organic spin ladder BIP-TENO is studied with an ultrahigh magnetic field of up to 150 T. Nontrivial multiple magnetization plateaus are observed, indicating there exist strong quantum correlations between spins. In addition to the previously reported 1/4 plateau, another plateau appears at 1/3 magnetization only when spins are decoupled to the lattice degree of freedom in the adiabatic limit. Spontaneous symmetry breaking is expected to occur with the spin-lattice decoupling induced by a fast evolution of external magnetic fields in the range of $\ensuremath{\mu}$s. Under the adiabatic condition, five fractional (1/4, 1/3, 1/2, 2/3, and 3/4) magnetization plateaus are likely to appear with an assumption that the magnetization saturates at around 160 T.

Entanglement of valence-bond-solid state models on topological surfaces

We investigated the scaling behaviors of entanglements on the two-leg ladder lattice structure implemented with Affleck–Kennedy–Lieb–Tasaki (AKLT) model on six types of topological surfaces, namely, torus, sphere, real projective plane, Klein bottle, cylinder and Möbius strip. All six topological surfaces on which our lattices were embedded are classified according to whether their boundaries are closed or open. Lattice structures on these topological surfaces are formed either by a trivalent or four-valent site to fulfill a complete spin-32 or spin-2 system, respectively. Their ground states, which are the valence-bond-solid states, are derived by the tensor-product method. The von Neumann entropies for entanglement of the bipartite region on all six topological surfaces are calculated and all results show that the entanglement entropies per area are bounded from above or below when approaching the thermodynamic limit. For the spin-2 and the spin-32 systems on all surfaces, except on the sphere, numerical results between even and odd cases of the number of lattice sites should be considered separately for scrutinizing their scaling behaviors. However, their entanglement entropies still satisfy the area law, but with a correction term.

Role of stochastic noise and generalization error in the time propagation of neural-network quantum states

Neural-network quantum states (NQS) have been shown to be a suitable variational ansatz to simulate out-of-equilibrium dynamics in two-dimensional systems using time-dependent variational Monte Carlo (t-VMC). In particular, stable and accurate time propagation over long time scales has been observed in the square-lattice Heisenberg model using the Restricted Boltzmann machine architecture. However, achieving similar performance in other systems has proven to be more challenging. In this article, we focus on the two-leg Heisenberg ladder driven out of equilibrium by a pulsed excitation as a benchmark system. We demonstrate that unmitigated noise is strongly amplified by the nonlinear equations of motion for the network parameters, which causes numerical instabilities in the time evolution. As a consequence, the achievable accuracy of the simulated dynamics is a result of the interplay between network expressiveness and measures required to remedy these instabilities. We show that stability can be greatly improved by appropriate choice of regularization. This is particularly useful as tuning of the regularization typically imposes no additional computational cost. Inspired by machine learning practice, we propose a validation-set based diagnostic tool to help determining optimal regularization hyperparameters for t-VMC based propagation schemes. For our benchmark, we show that stable and accurate time propagation can be achieved in regimes of sufficiently regularized variational dynamics.

Phase diagram of Rydberg-dressed atoms on two-leg square ladders: Coupling supersymmetric conformal field theories on the lattice

We investigate the phase diagram of hard-core bosons in two-leg ladders in the presence of soft-shoulder potentials. We show how the competition between local and non-local terms gives rise to a phase diagram with liquid phases with dominant cluster, spin-, and density-wave quasi-long-range ordering. These phases are separated by Berezinskii-Kosterlitz-Thouless, Gaussian, and supersymmetric (SUSY) quantum critical transitions. For the latter, we provide a phenomenological description of coupled SUSY conformal field theories, whose predictions are confirmed by matrix-product state simulations. Our results are motivated by, and directly relevant to, recent experiments with Rydberg-dressed atoms in optical lattices, where ladder dynamics has already been demonstrated, and emphasize the capabilities of these setups to investigate exotic quantum phenomena such as cluster liquids and coupled SUSY conformal field theories.

Probing Infinite Many-Body Quantum Systems with Finite-Size Quantum Simulators

Experimental studies of synthetic quantum matter are necessarily restricted to approximate ground states prepared on finite-size quantum simulators. In general, this limits their reliability for strongly correlated systems, for instance, in the vicinity of a quantum phase transition (QPT). Here, we propose a protocol that makes optimal use of a given finite-size simulator by directly preparing, on its bulk region, a mixed state representing the reduced density operator of the translation-invariant infinite-sized system of interest. This protocol is based on coherent evolution with a local deformation of the system Hamiltonian. For systems of free fermions in one and two spatial dimensions, we illustrate and explain the underlying physics, which consists of quasi-particle transport towards the system's boundaries while retaining the bulk "vacuum". For the example of a non-integrable extended Su-Schrieffer-Heeger model, we demonstrate that our protocol enables a more accurate study of QPTs. In addition, we demonstrate the protocol for an interacting spinful Fermi-Hubbard model with doping for 1D chains and a small two-leg ladder, where the initial state is a random superposition of energetically low-lying states.

Two-Hole Ground State: Dichotomy in Pairing Symmetry

A single-hole ground state Ansatz for the two-dimensional t-J model has been recently studied by the variational Monte Carlo (VMC) method. Such a doped hole behaves like a "twisted" non-Landau quasiparticle characterized by an emergent quantum number in agreement with exact numerics. In this work, we further investigate the ground state of two holes by VMC. It is found that the two holes strongly attract each other to form a pairing state with a new quantum number the same as obtained by the numerical exact diagonalization and density matrix renormalization group (DMRG) calculations. A unique feature of this pairing state is a dichotomy in the pairing symmetry, i.e., a d-wave in terms of the electron c operators and an s-wave in terms of the new quasiparticles, as explicitly illustrated in the ground state wave function. A similar VMC study of a two-hole wave function for the t-J two-leg ladder also yields a good agreement with the DMRG result. We demonstrate that the pairing mechanism responsible for the strong binding here is not due to the long-range antiferromagnetic order nor the resonating-valence-bound pairing in the spin background but is the consequence of the quantum phase-strings created by the hopping of holes. The resulting spin-current pattern mediating the pairing force is explicitly illustrated in the VMC calculation. Physical implications to superconductivity at finite doping are also discussed.