arXiv subjects

Bradraj Pandey

Publications and source records attributed to Bradraj Pandey.

At least 19 recordsLinked to original sources

arXiv2026

Kinetic obstruction to pairing in the doped Kitaev-Heisenberg ladder

We investigate the hole-doped Kitaev-Heisenberg ($t$-$J$-$K$) model on a two-leg ladder geometry using the density-matrix renormalization group (DMRG). We first consider the behavior of the antiferromagnetic Kitaev (AFK) spin-liquid phase as a function of hopping strength $t$ and doping level. This reveals intriguing pairing tendencies only for $\frac{t}{K} \lesssim 0.65$, consistent with prior results on three-leg ladders, and firmly supports the emerging picture that the physics of doped Kitaev spin liquids strongly depends on the kinetic energy of the doped holes. Analysis of one- and two-hole doping uncovers close links between the spatial profiles of the plaquette operator and the charge density. We construct a doping-dependent phase diagram for antiferromagnetic Heisenberg interactions and intermediate hopping $t=1$. Upon doping, the rung-singlet region develops dominant superconducting correlations. Charge-density-wave correlations dominate at weak doping near the transition to the stripy phase. Spin-density wave-like behavior is found in the AFK and ferromagnetic Kitaev limits, and in the stripy phase.

cond-mat.str-el↗

arXiv2025

Simulation of Topological $X$-Gates via Braiding of Majorana Zero Modes in an Interacting Quantum Dot System

Recent advances in quantum dot platforms have opened new pathways for realizing Majorana zero modes (MZMs) and simulating topological quantum computation. Here we propose an experimentally feasible setup for implementing topological $\sqrt{X}$- and $X$-quantum gates in an interacting $Y$-shaped quantum-dot array. The proposed novel architecture enables both braiding and charge readout through simple fusion operations controlled by gate-tunable potentials. Using many-body time-dependent simulations based on exact diagonalization, we analyze the braiding and fusion dynamics of MZMs in the presence of nearest-neighbor Coulomb interactions and pairing disorder. We compute diabatic errors, braiding fidelity, and the time- and space-resolved electron and hole components of the local density of states to monitor the braiding process. Our results show that even weak interactions or pairing disorder induce oscillations in the braiding fidelity, thereby setting an upper bound on the braiding speed. Furthermore, we demonstrate that comparing fusion outcomes before and after braiding provides a direct and experimentally accessible signature of the non-Abelian nature of MZMs in quantum dot systems.

cond-mat.str-el↗

arXiv2025

Diabatic error and propagation of Majorana zero modes in interacting quantum dots systems

Motivated by recent experimental progress in realizing Majorana zero modes (MZMs) using quantum dot systems, we investigate the diabatic errors associated with the movement of those MZMs. The movement is achieved by tuning time-dependent gate potentials applied to individual quantum dots, effectively creating a moving potential wall. To probe the optimized movement of MZMs, we calculate the experimentally accessible local density-of-states and time-dependent fidelity using many-body time-dependent numerical methods. Our analysis reveals that an optimal potential wall height is crucial to preserve the well-localized nature of the MZM during its movement. Moreover, for the first time, we analyze diabatic errors in realistic quantum-dot systems, incorporating the effects of repulsive Coulomb interactions and disorder in both hopping and pairing terms. Additionally, we provide a comparative study of diabatic errors arising from the simultaneous versus sequential tuning of multiple gates during the MZMs movement. Finally, we estimate the time scale required for MZM transfer in a six-quantum-dot system, demonstrating that MZM movement is feasible and can be completed well within the qubit's operational lifetime in practical quantum-dot setups.

cond-mat.mes-hall↗

arXiv2025

Pairing tendencies in the doped Kitaev-Heisenberg model

We study the impact of hole-doping on the Kitaev-Heisenberg model on the honeycomb lattice. We investigate the pairing tendencies and correlation functions in the framework of a $t-J-K$ model using density matrix renormalization group calculations on three-leg cylinders. In the case of the pure Kitaev model, which realizes a quantum spin-liquid phase at half-filling, we find that binding of two holes only occurs at low values of the hopping, where the holes are slow. We have theoretically verified that pair formation occurs in the limit of immobile holes, where the pure Kitaev model remains exactly solvable. When we instead fix the hopping at an intermediate, more realistic, value, and vary the Heisenberg and Kitaev interaction strengths, we find pairing tendencies only in the Néel phase. This is in contrast to prior mean-field calculations, highlighting the importance of accounting for the kinetic energy of dopants in generalized Kitaev models. Interestingly, we also find signatures of pair-density wave formation over the studied range of model parameters, namely a periodic modulation of the charge density as well as the spin-spin and pair-pair correlations in real space. Moreover, we present a comparative study of the different correlations as a function of doping. We finally discuss the potential for experimentally observing the studied physics in quantum materials and heterostructures.

cond-mat.str-el↗

arXiv2024

Non-trivial fusion of Majorana zero modes in interacting quantum-dot arrays

Motivated by recent experimental reports of Majorana zero modes (MZMs) in quantum-dot systems at the ``sweet spot'', where the electronic hopping $t_h$ is equal to the superconducting coupling $Δ$, we study the time-dependent spectroscopy corresponding to the non-trivial fusion of MZMs. The expression non-trivial refers to the fusion of Majoranas from different original pairs of MZMs, each with well-defined parities. For the first time, we employ an experimentally accessible time-dependent real-space local density-of-states (LDOS) method to investigate the non-trivial MZMs fusion outcomes in canonical chains and in a Y-shape array of interacting electrons. In the case of quantum-dot chains where two pairs of MZMs are initially disconnected, after fusion we find equal-height peaks in the electron and hole components of the LDOS, signaling non-trivial fusion into both the vacuum $I$ and fermion $Ψ$ channels with equal weight. For $π$-junction quantum-dot chains, where the superconducting phase has opposite signs on the left and right portions of the chain, after the non-trivial fusion, we observed the formation of an exotic two-site MZM near the center of the chain, coexisting with another single-site MZM. Furthermore, we also studied the fusion of three MZMs in the Y-shape geometry. In this case, after the fusion we observed the novel formation of another exotic multi-site MZM, with properties depending on the connection and geometry of the central region of the Y-shape quantum-dot array.

cond-mat.mes-hall↗

arXiv2024

Dynamics and Fusion of Majorana Zero Modes in Quantum-dot based Interacting Kitaev Chains

Motivated by the recent experimental realization of a minimal Kitaev chain in quantum dot systems, we present our theoretical findings on the dynamics and fusion of MZMs at or near the $``$sweet spot" $t_h = Δ$ (where the fermionic hopping $t_h$ and superconducting coupling $Δ$ are equal). We investigated the dynamics and fusion of MZMs using time-dependent real-space local density-of-states methods. The movement of Majoranas and the detection of fusion channels are crucial for topological quantum computations. Additionally, we discuss our recent discovery of exotic $``$multi-site" MZMs in $Y$-shaped Kitaev wires, which is important for the potential braiding of Majoranas in $Y$-junctions formed from arrays of quantum dots. Finally, we present results on "non-trivial" fusion using canonical Kitaev wires at the sweet spot.

cond-mat.supr-con↗

arXiv2024

Crystalline-Symmetry-Protected Majorana Modes in Coupled Quantum Dots

We propose a minimalist architecture for achieving various crystalline-symmetry-protected Majorana modes in an array of coupled quantum dots. Our framework is motivated by the recent experimental demonstrations of two-site and three-site artificial Kitaev chains in a similar setup. We find that introducing a $π$-phase domain wall in the Kitaev chain leads to a pair of mirror-protected Majorana zero modes located at or near the junction. Joining two $π$-junctions into a closed loop, we can simulate two distinct classes of two-dimensional higher-order topological superconducting phases, both carrying symmetry-protected Majorana modes around the sample corners. As an extension of the $π$-junction, we further consider a general vertex structure where $n$ Kitaev chains meet, i.e., a Kitaev $n$-vertex. We prove that such an $n$-vertex, if respecting a dihedral symmetry group $D_n$, necessarily carries $n$ vertex-bound Majorana modes protected by the $D_n$ symmetry. Resilience of the junction and vertex Majorana bound states against disorder and correlation effects is also discussed. Our architecture paves the way for designing, constructing, and exploring a wide variety of artificial topological crystalline phases in experiments.

cond-mat.mes-hall↗

arXiv2023

Majorana zero modes in Y-shape interacting Kitaev wires

Motivated by the recent experimental realization of minimal Kitaev chains using quantum dots, we investigate the Majorana zero modes (MZM) in $Y$-shape Kitaev wires. We solve the associated Kitaev models analytically at the sweet spot ($t_h=Δ$) and derive the exact form of MZM wave-functions in this geometry. The novelty of our result is the observation of multi-site MZMs located near the junction center on the nearby edge sites of each leg. This result is important for potential braiding of Majoranas and the performance of $Y$-junctions made from arrays of quantum dots. Furthermore, we study the stability of local (single-site) and multi-site MZMs modes in the presence of Coulomb repulsion, using density matrix renormalization group theory. Our local density-of-states calculation shows that these multi-site MZMs are as equally topologically protected as the single-site MZMs when in the presence of Coulomb repulsion or when away from the sweet-spot.

cond-mat.supr-con↗

arXiv2022

Out of Equilibrium Majoranas in Interacting Kitaev Chains

We employ a time-dependent real-space local density-of-states method to study the movement and fusion of Majorana zero modes in the 1D interacting Kitaev model, based on the time evolution of many-body states. We analyze the dynamics and both fusion channels of Majoranas using time-dependent potentials, either creating {\it Walls} or {\it Wells}. % focusing on the local density-of-states and charge-density of fermions varying with time. For fast moving Majoranas, we unveil non-equilibrium signatures of the ``strong-zero mode'' operator (quasi parity degeneracy in the full spectrum) and its breakdown in the presence of repulsive Coulomb interactions. Focusing on forming a full electron after fusion, we also discuss upper and lower limits on the Majorana speed needed to reduce non-adiabatic effects and to avoid poisoning due to decoherence.

cond-mat.supr-con↗

arXiv2021

Excitonic wave-packet evolution in a two-orbital Hubbard model chain: A real-time real-space study

Motivated by experimental developments introducing the concept of spin-orbit separation, we study the real-space time evolution of an excitonic wave-packet using a two-orbital Hubbard model. The exciton is created by exciting an electron from a lower energy half-filled orbital to a higher energy empty orbital. We carry out the real-time dynamics of the resulting excitonic wave-packet, using the time-dependent density matrix renormalization group method. We find clear evidence of charge-spin and spin-orbit separation in real-space, by tracking the time evolution of local observables. We show that the velocity of the orbiton can be tuned by varying the inter-orbital interactions. We also present a comparative study of a hole (in one orbital) and exciton (in two orbitals) dynamics in one-dimensional systems. Moreover, we analyze the dynamics of an exciton with spin-flip excitation, where we observe fractionalized spinons induced by Hund's interaction.

cond-mat.str-el↗

arXiv2021

Intertwined charge, spin, and pairing orders in doped iron ladders

Motivated by recent experimental progress on iron-based ladder compounds, we study the doped two-orbital Hubbard model for the two-leg ladder BaFe$_2$S$_3$. The model is constructed by using {\it ab initio} hopping parameters and the ground state properties are investigated using the density matrix renormalization group method. We show that the $(π,0)$ magnetic ordering at half-filling, with ferromagnetic rungs and antiferromagnetic legs, becomes incommensurate upon hole doping. Moreover, depending on the strength of the Hubbard $U$ coupling, other magnetic patterns, such as $(0,π)$, are also stabilized. We found that the binding energy for two holes becomes negative for intermediate Hubbard interaction strength, indicating hole pairing. Due to the crystal-field split among orbitals, the holes primarily reside in one orbital, with the other one remaining half-filled. This resembles orbital selective Mott states. The formation of tight hole pairs continues with increasing hole density, as long as the magnetic order remains antiferromagnetic in one direction. The study of pair-pair correlations indicates the dominance of the intra-orbital spin-singlet channel, as opposed to other pairing channels. Although in a range of hole doping pairing correlations decay slowly, our results can also be interpreted as corresponding to a charge-density-wave made of pairs, a precursor of eventual superconductivity after interladder couplings are included. Such scenario of intertwined orders has been extensively discussed before in the cuprates, and our results suggest a similar physics could exist in ladder iron-based superconductors. Finally, we also show that a robust Hund's coupling is needed for pairing to occur.

cond-mat.str-el↗

arXiv2020

Quench dynamics of two component dipolar fermions subject to a quasiperiodic potential

Motivated by recent experiments in fermionic polar gases, we study the non-equilibrium dynamics of two-component dipolar fermions subject to a quasiperiodic potential. We investigate the localization of charge and spin degrees of freedom time evolving with a long-range spin-SU(2) symmetric fermionic Hamiltonian, by calculating experimentally accessible dynamical observables. To study the non-equilibrium dynamics, we start the time evolution with two initial states at half-filling: (i) product state with doublons $|\uparrow \downarrow 0 \uparrow \downarrow 0 \uparrow \downarrow 0 \uparrow \downarrow 0 \uparrow \downarrow \rangle$ and (ii) product state with singlons $|\uparrow \ \downarrow \ \uparrow \ \downarrow \ \uparrow \ \downarrow \ \uparrow \ \downarrow \ \uparrow \ \downarrow \ \rangle$. We carried out the real-time evolution via the fermionic Hamiltonian using exact diagonalization(ED) and the time-dependent variational principle (TDVP) for finite Matrix product states(MPSs), within experimentally relevant time scales. For the product state with doublons, we observe a delocalized to localized phase transition varying disorder strengths, by monitoring the decay of charge imbalance with time. For the long-range interacting Hamiltonian of our focus, and in the presence of strong enough disorder, starting the time evolution with singlons we find a strong reduction in the spin delocalization, contrary to results of previous studies using the disordered short-range (on-site) Hubbard model with SU(2) symmetry. Our predictions for localization of both charge and spin should be observable in ultra-cold experiments with fermionic dipolar atoms subject to a quasiperiodic potential.

cond-mat.quant-gas↗

arXiv2020

Origin of the Magnetic and Orbital ordering in $α$-Sr$_2$CrO$_4$

Motivated by recent experimental progress in transition metal oxides with the K$_2$NiF$_4$ structure, we investigate the magnetic and orbital ordering in $α$-Sr$_2$CrO$_4$. Using first principles calculations, first we derive a three-orbital Hubbard model, which reproduces the {\it ab initio} band structure near the Fermi level. The unique reverse splitting of $t_{2g}$ orbitals in $α$-Sr$_2$CrO$_4$, with the $3d^2$ electronic configuration for the Cr$^{4+}$ oxidation state, opens up the possibility of orbital ordering in this material. Using real-space Hartree-Fock for multi-orbital systems, we constructed the ground-state phase diagram for the two-dimensional compound $α$-Sr$_2$CrO$_4$. We found stable ferromagnetic, antiferromagnetic, antiferro-orbital, and staggered orbital stripe ordering in robust regions of the phase diagram. Furthermore, using the density matrix renormalization group method for two-leg ladders with the realistic hopping parameters of $α$-Sr$_2$CrO$_4$, we explore magnetic and orbital ordering for experimentally relevant interaction parameters. Again, we find a clear signature of antiferromagnetic spin ordering along with antiferro-orbital ordering at moderate to large Hubbard interaction strength. We also explore the orbital-resolved density of states with Lanczos, predicting insulating behavior for the compound $α$-Sr$_2$CrO$_4$, in agreement with experiments. Finally, an intuitive understanding of the results is provided based on a hierarchy between orbitals, with $d_{xy}$ driving the spin order, while electronic repulsion and the effective one dimensionality of the movement within the $d_{xz}$ and $d_{yz}$ orbitals driving the orbital order.

cond-mat.str-el↗

arXiv2020

Prediction of exotic magnetic states in the alkali metal quasi-one-dimensional iron selenide compound Na$_2$FeSe$_2$

The magnetic and electronic phase diagram of a model for the quasi-one-dimensional alkali metal iron selenide compound Na$_2$FeSe$_2$ is presented. The novelty of this material is that the valence of iron is Fe$^{2+}$ contrary to most other iron-chain compounds with valence Fe$^{3+}$. Using first-principles techniques, we developed a three-orbital tight-binding model that reproduces the {\it ab initio} band structure near the Fermi level. Including Hubbard and Hund couplings and studying the model via the density matrix renormalization group and Lanczos methods, we constructed the ground state phase diagram. A robust region where the block state $\uparrow \uparrow \downarrow \downarrow \uparrow \uparrow \downarrow \downarrow$ is stabilized was unveiled. The analog state in iron ladders, employing 2$\times$2 ferromagnetic blocks, is by now well-established, but in chains a block magnetic order has not been observed yet in real materials. The phase diagram also contains a large region of canonical staggered spin order $\uparrow \downarrow \uparrow \downarrow \uparrow \downarrow \uparrow$ at very large Hubbard repulsion. At the block to staggered transition region, a novel phase is stabilized with a mixture of both states: an inhomogeneous orbital-selective charge density wave with the exotic spin configuration $\uparrow \uparrow \downarrow \uparrow \downarrow \downarrow \uparrow \downarrow$. Our predictions for Na$_2$FeSe$_2$ may guide crystal growers and neutron scattering experimentalists towards the realization of block states in one-dimensional iron-selenide chain materials.

cond-mat.str-el↗

arXiv2019

Quantum Hall Skyrmions at $ν=0,\pm 1$ in monolayer graphene

Monolayer graphene under a strong perpendicular field exhibit quantum Hall ferromagnetism with spontaneously broken spin and valley symmetry. The approximate SU(4) spin/valley symmetry is broken by small lattice scale effects in the central Landau level corresponding to filling factors $ν=0,\pm 1$. Notably the ground state at $ν=0$ is believed to be a canted antiferromagnetic (AF) or a ferromagnetic (F) state depending on the component of the magnetic field parallel to the layer and the strength of small anisotropies. We study the skyrmions for the filling factors $ν=\pm 1,0$ by using exact diagonalizations on the spherical geometry. If we neglect anisotropies we confirm the validity of the standard skyrmion picture generalized to four degrees of freedom. For filling factor $ν=- 1$ the hole skyrmion is an infinite-size valley skyrmion with full spin polarization because it does not feel the anisotropies. The electron skyrmion is also always of infinite size. In the F phase it is always fully polarized while in the AF phase it undergoes continuous magnetization under increasing Zeeman energy. In the case of $ν=0$ the skyrmion is always maximally localized in space both in F and AF phase. In the F phase it is fully polarized while in the AF it has also progressive magnetization with Zeeman energy. The magnetization process is unrelated to the spatial profile of the skyrmions contrary to the SU(2) case. In all cases the skyrmion physics is dominated by the competition between anisotropies and Zeeman effect but not directly by the Coulomb interactions, breaking universal scaling with the ratio Zeeman to Coulomb energy.

cond-mat.str-el↗

arXiv2018

Quantum purification spectroscopy

We discuss a protocol based on quenching a purified quantum system that allows to capture bulk spectral features. It uses an infinite temperature initial state and an interferometric strategy to access the Loschmidt amplitude, from which the spectral features are retrieved via Fourier transform, providing coarse-grained approximation at finite times. It involves techniques available in current experimental setups for quantum simulation, at least for small systems. We illustrate possible applications in testing the eigenstate thermalization hypothesis and the physics of many-body localization.

quant-ph↗

arXiv2017

Triplet Superfluidity on a triangular ladder with dipolar fermions

Motivated by recent experimental progress in the field of dipolar-Fermi gases, we investigate the quantum phases of dipolar fermions, on a triangular ladder at half filling. Using density matrix renormalization group method, in presence of onsite repulsion and intersite attractive interaction, we find exotic spin-triplet superfluid phase in addition to the usual spin-density and charge-density waves. We examine the stability of spin-triplet superfluid phase by varying hopping along the rungs of the triangle. Possibility of fermionic supersolidity has also been discussed, by considering three- body interaction in the Hamiltonian. We also study the effect of spin-dependent hopping on the stability of spin-triplet superfluid phase.

cond-mat.str-el↗

arXiv2016

Breakdown of electron-pairs in the presence of an electric field of a superconducting ring

The quantum dynamics of quasi-one-dimensional ring with varying electron filling factor is investigated in presence of external electric field. The system is modeled within Hubbard Hamiltonian with attractive Coulomb correlation, which results in superconducting ground state when away from half-filling. The electric field is induced by applying time-dependent Aharonov-Bohm flux in the perpendicular direction. To explore the non-equilibrium phenomena arising from the field, we adopt exact diagonalization and Crank-Nicolson numerical method. With increase in electric field strength, the electron pairs, a signature of superconducting phase, start breaking and the system enters into a metallic phase. However, the strength of the electric field for this quantum phase transition depends on the electronic correlation. This phenomenon has been confirmed by flux-quantization of time-dependent current and pair correlation functions

cond-mat.supr-con↗