arXiv subjects

Sk Saniur Rahaman

Publications and source records attributed to Sk Saniur Rahaman.

7 recordsLinked to original sources

arXiv2026

Excitation Spectra of the Frustrated Spin-1/2 $J_1$-$J_2$ Model via Dual Spin-Sector Variational Quantum Eigensolvers

Finding excited states and excitation gaps in frustrated spin systems using Variational Quantum Eigensolvers (VQE) is complicated by state-ordering inversions. In the frustrated spin-1/2 $J_1$-$J_2$ Heisenberg model, standard single-sector algorithms like Variational Quantum Deflation (VQD) in $S_z=0$ fail when $J_2/J_1 < 0.25$. In this regime, the lowest-lying excitation in $S_z=0$ is a Triplet ($S=1$), which lies below the Excited Singlet ($S=0$). Standard deflation projects out the ground singlet and converges onto the Triplet state, misidentifying it as the Excited Singlet. Here, this work presents a Dual Spin-Sector VQE framework that resolves these state-ordering inversions applied to frustrated $J_1-J_2$ models on 1D spin chains and 2D rectangular lattices. Firstly, by optimizing the ground Triplet state in the $S_z=1$ sector (where singlet states cannot exist), mapping it into $S_z=0$ via the total spin-lowering operator $S^- = \sum_i S_i^-$, and evaluating a dual-sector penalty cost function, the Excited Singlet ($E_S$) is isolated without variational ambiguity. Numerical state-vector simulations confirm exact convergence to machine precision with unit overlap fidelity. The method captures key physical features, including the gapless phase, the gapless-gapped critical point at $J_2/J_1 \approx 0.2411$, the Majumdar-Ghosh dimer point ($J_2/J_1 = 0.50$), and the 2D non-magnetic frustrated regime ($J_2/J_1 \approx 0.40 - 0.60$). Finite-shot sampling simulations and gate-scaling analytics up to $N=100$ qubits demonstrate the resource efficiency and shot resilience of the algorithm for near-term quantum execution.

cond-mat.str-el↗

arXiv2026

Strong Dimerization and Field-Induced Reconstruction of the Low-Energy Spectrum in $\mathrm{Cu}_3(\mathrm{OH})_4(\mathrm{HCO}_2)_2$

We investigate the field-dependent low-energy thermodynamics of the distorted triangular quantum antiferromagnet $\mathrm{Cu}_3(\mathrm{OH})_4(\mathrm{HCO}_2)_2$ using a sector-resolved Superblock Diagonalization Method (SBDM) supplemented by a transfer-matrix treatment of weakly coupled layers. The strong exchange hierarchy, dominated by the Cu1--Cu1 intradimer coupling $J_2=150\,\mathrm{K}$, separates a high-energy dimer sector from a much softer magnetic manifold formed predominantly by the Cu2 moments. In the 24-site cluster, sixteen Cu1 spins form the strongly bound sector while eight Cu2 spins remain magnetically active; polarization of these eight spins gives $S^z=4$ compared with $S^z_{\rm sat}=12$, providing a direct microscopic origin for the one-third magnetization scale. The finite-temperature thermodynamics reveals a non-monotonic field evolution of the low-energy scale: the dominant $C/T$ feature softens with increasing field, reaches a minimum near the field region around $2\,\mathrm{T}$, and subsequently hardens as the low-temperature magnetization approaches $M_{\rm sat}/3$. Temperature and field sweeps thus expose a common field-induced spectral reconstruction, while the strongly reduced entropy reflects the restricted number of thermally active degrees of freedom below the dimer excitation scale. Our results identify strong-dimer-induced reduction of the active magnetic Hilbert space, followed by field-driven reorganization of the residual spin sector, as the common microscopic origin of the one-third magnetic response and the non-monotonic low-temperature thermodynamics.

cond-mat.str-el↗

arXiv2026

Covariance Geometry of Basis-Resolved Low-Energy Wavefunctions in the Spin-$1/2$ Kitaev--Heisenberg Model

We develop a basis-resolved covariance framework for investigating the organization of low-energy many-body wavefunctions in the spin-$1/2$ Kitaev--Heisenberg model. By constructing covariance matrices from local-spin, bond-correlation, and plaquette-flux representations of the low-energy states, Principal Component Analysis (PCA) is employed to identify the dominant collective covariance modes. We find a systematic evolution of the covariance geometry across the phase diagram: magnetically ordered phases are described by an essentially one-dimensional covariance manifold, conventional magnetic phase boundaries exhibit competition between leading covariance modes, whereas the Kitaev regimes develop intrinsically multidimensional covariance geometry. Furthermore, the same many-body wavefunction produces distinct covariance geometries in different operator representations, demonstrating that covariance geometry is determined jointly by the quantum state and the physical observables used to probe it. Shannon entropy and the participation ratio provide quantitative measures of this evolution. The present framework establishes basis-resolved covariance geometry as a complementary statistical perspective for characterizing frustrated quantum many-body systems beyond conventional order parameters.

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arXiv2024

Magnetic plateaus and jumps in a spin-1/2 ladder with alternate Ising-Heisenberg rungs: a field dependent study

We study a frustrated two-leg spin-1/2 ladder with alternate Ising and isotropic Heisenberg rung exchange interactions, whereas, interactions along legs and diagonals are Ising type. The ground-state (GS) of this model has four exotic phases: (i) the stripe rung ferromagnet (SRFM), (ii) the anisotropic anti-ferromagnet (AAFM), (iii) the Dimer, and (iv) the stripe leg ferromagnet (SLFM) in absence of any external magnetic field. In this work, we study the effect of externally applied longitudinal and transverse fields on GS phases and note that there are two plateaus with per-site magnetization $1/4$ and $1/2$. There is another plateau at zero magnetization due to a finite spin gap in the presence of a longitudinal field. The exact diagonalization (ED) and the transfer matrix (TM) methods are used to solve the model Hamiltonian and the mechanism of plateau formation is analyzed using spin density, quantum fidelity, and quantum concurrence. In the (i) SRFM phase, Ising exchanges are dominant for all spins but the Heisenberg rungs are weak, and therefore, the magnetization shows a continuous transition as a function of the transverse field. In the other three phases [(ii)-(iv)], the Ising dimer rungs are weak and those are broken first to reach a plateau with per-site magnetization $1/4$, having a large gap which is closed by further application of the transverse field.

cond-mat.str-el↗

arXiv2022

Study of the Berezinskii-Kosterlitz-Thouless transition: An unsupervised machine learning approach

The Berezinskii-Kosterlitz-Thouless (BKT) transition in magnetic system is an intriguing phenomena and an accurate estimation of the BKT transition temperature has been a long-standing problem. In this work we explore the anisotropic classical Heisenberg XY and XXZ models with ferromagnetic exchange on a square lattice and antiferromagnetic exchange on a triangular lattice using an unsupervised machine learning approach called principal component analysis (PCA). In earlier studies of the BKT transition, spin configurations and vorticities calculated from Monte Carlo method are used to determine the transition temperature $T_{BKT}$, but those methods fail to give any conclusive results by analyzing the principal components in the PCA approach. In this work vorticities are used as initial input to the PCA and curve of the first principal component with temperature is fitted with a function to determine an accurate value of $T_{BKT}$. This procedure works well for anisotropic classical Heisenberg with ferromagnetic exchange on square lattice as well as for frustrated antiferromagnetic exchange on a triangular lattice. The classical anisotropic Heisenberg antiferromagnetic model on the triangular lattice has two close transitions; the BKT at $T_{BKT}$ and Ising like phase transition for chirality at $T_c$ and it is difficult to separate these transition points. It is also noted that using the PCA method and manipulation of their first principal component, not only separation of transition points are possible but also transition temperature can be determined accurately.

cond-mat.str-el↗

arXiv2022

Machine learning approach to study quantum phases of a frustrated one dimensional spin-1/2 system

Frustration driven quantum fluctuation leads to many exotic phases in the ground state and study of these quantum phase transitions is one of the most challenging areas of research in condensed matter physics. Here, a frustrated Heisenberg $J_1-J_2$ model of spin-1/2 chain with nearest exchange interaction $J_1$ and next nearest exchange interaction $J_2$ is studied using the principal component analysis (PCA) which is an unsupervised machine learning technique. In this method most probable spin configurations (MPSC) of ground-state (GS) and first excited state (FES) for different $J_2/J_1$ are used as the input in PCA to construct the co-variance matrix. The `quantified principal component' of the largest eigenvalue of co-variance matrix $p_1(J_2/J_1)$ is calculated and it is shown that the nature and variation of $p_1(J_2/J_1)$ can accurately predict the phase transitions and degeneracies in the GS. The $p_1(J_2/J_1)$ calculated from the MPSC of GS can only exhibit the signature of degeneracies in the GS, whereas, $p_1(J_2/J_1)$ calculated from MPSC of FES captures the gapless spin liquid (GSL)-dimer phase transition as well as all the degeneracies of the model system. We show that jump in $p_1(J_2/J_1)$ of FES at $J_2/J_1 \approx 0.241$, indicates the GSL-dimer phase transition, whereas its kinks give the signature of the GS degeneracies. The scatter plot of first two principal components of FES shows distinct band formation for different phases.

cond-mat.str-el↗

arXiv2020

Ground state properties and exact thermodynamics of a 2-leg anisotropic spin ladder system

We study a frustrated two-leg spin ladder with alternate isotropic Heisenberg and Ising rung exchange interactions, whereas, interactions along legs and diagonals are Ising-type. All the interactions in the ladder are anti-ferromagnetic in nature and induce frustration in the system. This model shows four interesting quantum phases: (i) stripe rung ferromagnetic (SRFM), (ii) stripe rung ferromagnetic with edge singlet (SRFM-E), (iii) anisotropic antiferromagnetic (AAFM), and (iv) stripe leg ferromagnetic (SLFM) phase. We construct a quantum phase diagram for this model and show that in stripe rung ferromagnet (SRFM), the same type of sublattice spins (either $S$ or $σ$-type spins) are aligned in the same direction. Whereas, in anisotropic antiferromagnetic phase, both $S$ and $σ$-type of spins are anti-ferromagnetically aligned with each other, two nearest $S$ spins along the rung form an anisotropic singlet bond whereas two nearest $σ$ spins form an Ising bond. In large Heisenberg rung exchange interaction limit, spins on each leg are ferromagnetically aligned, but spins on different legs are anti-ferromagnetically aligned. The thermodynamic quantities like $Cv(T)$, $χ(T)$ and $S(T)$ are also calculated using the transfer matrix method for different phase. The magnetic gap in the SRFM and the SLFM can be notice from $χ(T)$ and $Cv(T)$ curves.

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