Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1705.07293 · Physical review. B./Physical review. B

Quantum phases of frustrated two-leg spin- 12 ladders with skewed rungs

Geetanjali Giri, Dayasindhu Dey, Manoranjan Kumar, S. Ramasesha, Z. G. Soos

Published Jun 6, 2017• 24 citations
arXivHTMLPDF

Abstract

The quantum phases of two-leg spin-$\frac{1}{2}$ ladders with skewed rungs are obtained using exact diagonalization of systems with up to 26 spins and by density-matrix renormalization-group calculations to 500 spins. The ladders have isotropic antiferromagnetic (AF) exchange ${J}_{2}>0$ between first neighbors in the legs, variable isotropic AF exchange ${J}_{1}$ between some first neighbors in different legs, and an unpaired spin per odd-membered ring when ${J}_{1}\ensuremath{\gg}{J}_{2}$. Ladders with skewed rungs and variable ${J}_{1}$ have frustrated AF interactions leading to multiple quantum phases: AF at small ${J}_{1}$, either ferromagnetic or AF at large ${J}_{1}$, as well as bond-order-wave phases or reentrant AF (singlet) phases at intermediate ${J}_{1}$.

DOI
10.1103/physrevb.95.224408

Related papers

Quantum phases of a frustrated spin-1 system: The 5/7 skewed ladder

Sambunath Das, Dayasindhu Dey, Manoranjan Kumar +1 more

The quantum phases in a spin-1 skewed ladder system formed by alternately fusing five- and seven-membered rings are studied numerically using the exact diagonalization technique up to 16 spins and using the density matrix renormalization group method for larger system sizes. The ladder has a fixed isotropic antiferromagnetic (AF) exchange interaction (${J}_{2}=1$) between the nearest-neighbor spins along the legs and a varying isotropic AF exchange interaction (${J}_{1}$) along the rungs. As a function of ${J}_{1}$, the system shows many interesting ground states (gs) which vary from different types of nonmagnetic and ferrimagnetic gs. The study of various gs properties such as spin gap, spin-spin correlations, spin density, and bond order reveal that the system has four distinct phases, namely, the AF phase at small ${J}_{1}$; the ferrimagnetic phase with gs spin ${S}_{G}=n$ for $1.44<{J}_{1}<4.74$ and with ${S}_{G}=2n$ for ${J}_{1}>5.63$, where $n$ is the number of unit cells; and a reentrant nonmagnetic phase at $4.74<{J}_{1}<5.44$. The system also shows the presence of spin current at specific ${J}_{1}$ values due to simultaneous breaking of both reflection and spin parity symmetries.

arXiv:2012.07486•Physical review. B./Physical review. B•Sep 27, 2021•4 citations

Singlet quantum phases and magnetization of the frustrated spin-1/2 ladder with ferromagnetic (F) exchange in legs and alternating F-AF exchange in rungs

Chatterjee, Monalisa, Manoranjan Kumar, Z. G. Soos

The magnetization $M(h)$ is used to identify three singlet quantum phases of the ladder with isotropic exchange interactions. The Dimer phase with frustrated F exchanges in rungs and legs has a first-order $M(h)$ transition at $0$ K from singlet to ferromagnetic at the saturation field $h_s$. The Haldane-DAF phase with strong F exchange in rungs and net AF exchange between rungs has continuous $M(h)$ and is adiabatically connected to the $S = 1$ Heisenberg AF chain. The AF phase with strong F exchange in legs and net AF exchange between legs has continuous $M(h)$ and is adiabatically connected to the spin-1/2 $J_1-J_2$ model with $J_1 > 0$ and $J_2 < 0$. All three singlet phases have finite gaps to the lowest triplet state.

arXiv:2305.12884•May 22, 2023•1 citation

Spin-1/2 string correlations and singlet-triplet gaps of frustrated ladders with ferromagnetic (F) legs and alternate F and AF rungs

Chatterjee, Monalisa, Manoranjan Kumar, Z. G. Soos

The frustrated ladder with alternate ferromagnetic(F) exchange $-J_F$ and AF exchange $J_A$ to first neighbors and F exchange $-J_L$ to second neighbors is studied by exact diagonalization (ED) and density matrix renormalization group (DMRG) calculations in systems of $2N$ spins-1/2 with periodic boundary conditions. The ground state is a singlet $(S = 0)$ and the singlet-triplet gap $\varepsilon_T$ is finite for the exchanges considered. Spin-1/2 string correlation functions $g_1(N)$ and $g_2(N)$ are defined for an even number $N$ of consecutive spins in systems with two spins per unit cell; the ladder has string order $g_2(\infty)> 0$ and $g_1(\infty) = 0$. The minimum $N^*$ of $g_2(N)$ is related to the range of ground-state spin correlations. Convergence to $g_2(\infty)$ is from below, and $g_1(N)$ decreases exponentially for $N \geq N^*$. Singlet valence bond (VB) diagrams account for the size dependencies. The frustrated ladder at special values of $J_F$, $J_L$ and $J_A$ reduces to well-known models such as the spin-1 Heisenberg antiferromagnet and the $J_1-J_2$ model, among others. Numerical analysis of ladders matches previous results for spin-1 gaps or string correlation functions and extends them to spin-1/2 systems. The nondegenerate singlet ground state of ladder is a bond-order wave, a Kekulé VB diagrams at $J_L = J_F/2 \leq J_A$, that is reversed on interchanging $-J_F$ and $J_A$. Inversion symmetry is spontaneously broken in the dimer phase of the $J_1-J_2$ model where the Kekulé diagrams are the doubly degenerate ground states at $J_2/J_1 = 1/2$.

arXiv:2403.05238•Mar 8, 2024•0 citations

Singlet quantum phases of the frustrated spin-1/2 ladder with ferromagnetic (F) exchange in legs and alternating F-AF exchange in rungs

Monalisa Chatterjee, Manoranjan Kumar, Z. G. Soos

Abstract Ladders with 2 N spins-1/2 and singlet ( S = 0) ground states are studied numerically using exact diagonalization and density matrix renormalization group (DMRG) calculations. The curvatures E ″ ( s ) of states with the lowest energy E ( s ) at spin s = S / N ≤ 1 are obtained in the thermodynamic limit. All states have E ″ ( s ) > 0 in two phases, one with strong F exchange J F in rungs, the other with strong F exchange J L in legs. The Dimer phase with frustrated F exchanges has one or more states with E ″ ( s ) < 0. All three phases have finite gaps to the lowest triplet state. The ladder at J F → ∞ is adiabatically connected to the spin-1 Heisenberg AF chain, and at J L → ∞ to the J 1 − J 2 model.

Physica Scripta•Dec 22, 2023•3 citations

Spin- 12 string correlations and singlet-triplet gaps of frustrated ladders with ferromagnetic legs and alternate ferromagnetic and antiferromagnetic rungs

Monalisa Chatterjee, Manoranjan Kumar, Z. G. Soos

The frustrated ladder with alternate ferromagnetic exchange $\ensuremath{-}{J}_{F}$ and antiferromagnetic exchange ${J}_{A}$ to first neighbors and ferromagnetic exchange $\ensuremath{-}{J}_{L}$ to second neighbors is studied by exact diagonalization and density matrix renormalization group calculations in systems of $2N$ spins-$\frac{1}{2}$ with periodic boundary conditions. The ground state is a singlet $(S=0)$ and the singlet-triplet gap ${\ensuremath{\varepsilon}}_{T}$ is finite for the exchanges considered. Spin-$\frac{1}{2}$ string correlation functions ${g}_{1}(N)$ and ${g}_{2}(N)$ are defined for an even number $N$ of consecutive spins in systems with two spins per unit cell; the ladder has string order ${g}_{2}(\ensuremath{\infty})>0$ and ${g}_{1}(\ensuremath{\infty})=0$. The minimum ${N}^{*}$ of ${g}_{2}(N)$ is related to the range of ground-state spin correlations. Convergence to ${g}_{2}(\ensuremath{\infty})$ is from below, and ${g}_{1}(N)$ decreases exponentially for $N\ensuremath{\ge}{N}^{*}$. Singlet valence bond (VB) diagrams account for the size dependencies. The frustrated ladder at special values of ${J}_{F}, {J}_{L}$, and ${J}_{A}$ reduces to well-known models such as the spin-1 Heisenberg antiferromagnet and the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model, among others. Numerical analysis of ladders matches previous results for spin-1 gaps or string correlation functions and extends them to spin-$\frac{1}{2}$ systems. The nondegenerate singlet ground state of the ladder is a bond-order wave, a Kekul\'e VB diagram at ${J}_{L}={J}_{F}/2\ensuremath{\le}{J}_{A}$, that is reversed on interchanging $\ensuremath{-}{J}_{F}$ and ${J}_{A}$. Inversion symmetry is spontaneously broken in the dimer phase of the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model where the Kekul\'e diagrams are the doubly degenerate ground states at ${J}_{2}/{J}_{1}=1/2$.

Physical review. B./Physical review. B•Mar 28, 2024•1 citation

Quantum phases and thermodynamics of a frustrated spin-1/2 ladder with alternate Ising–Heisenberg rung interactions

Sk Saniur Rahaman, Shaon Sahoo, Manoranjan Kumar

Abstract 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 isotropic S -type or discrete anisotropic 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 specific heat C v ( T ), magnetic susceptibility χ ( T ) and thermal entropy S ( T ) are also calculated using the transfer matrix method for various phases. The magnetic gap in the SRFM and the SLFM can be noticed from χ ( T ) and C v ( T ) curves.

Journal of Physics Condensed Matter•Apr 15, 2021•0 citations
The quantum phases of two-leg spin-12\frac{1}{2}21​ ladders with skewed rungs are obtained using exact diagonalization of systems with up to 26 spins and by density-matrix renormalization-group calculations to 500 spins. The ladders have isotropic antiferromagnetic (AF) exchange J2>0{J}_{2}>0J2​>0 between first neighbors in the legs, variable isotropic AF exchange J1{J}_{1}J1​ between some first neighbors in different legs, and an unpaired spin per odd-membered ring when J1\ensuremath≫J2{J}_{1}\ensuremath{\gg}{J}_{2}J1​\ensuremath≫J2​. Ladders with skewed rungs and variable J1{J}_{1}J1​ have frustrated AF interactions leading to multiple quantum phases: AF at small J1{J}_{1}J1​, either ferromagnetic or AF at large J1{J}_{1}J1​, as well as bond-order-wave phases or reentrant AF (singlet) phases at intermediate J1{J}_{1}J1​.
The quantum phases in a spin-1 skewed ladder system formed by alternately fusing five- and seven-membered rings are studied numerically using the exact diagonalization technique up to 16 spins and using the density matrix renormalization group method for larger system sizes. The ladder has a fixed isotropic antiferromagnetic (AF) exchange interaction (J2=1{J}_{2}=1J2​=1) between the nearest-neighbor spins along the legs and a varying isotropic AF exchange interaction (J1{J}_{1}J1​) along the rungs. As a function of J1{J}_{1}J1​, the system shows many interesting ground states (gs) which vary from different types of nonmagnetic and ferrimagnetic gs. The study of various gs properties such as spin gap, spin-spin correlations, spin density, and bond order reveal that the system has four distinct phases, namely, the AF phase at small J1{J}_{1}J1​; the ferrimagnetic phase with gs spin SG=n{S}_{G}=nSG​=n for 1.44<J1<4.741.44<{J}_{1}<4.741.44<J1​<4.74 and with SG=2n{S}_{G}=2nSG​=2n for J1>5.63{J}_{1}>5.63J1​>5.63, where nnn is the number of unit cells; and a reentrant nonmagnetic phase at 4.74<J1<5.444.74<{J}_{1}<5.444.74<J1​<5.44. The system also shows the presence of spin current at specific J1{J}_{1}J1​ values due to simultaneous breaking of both reflection and spin parity symmetries.
The magnetization M(h)M(h)M(h) is used to identify three singlet quantum phases of the ladder with isotropic exchange interactions. The Dimer phase with frustrated F exchanges in rungs and legs has a first-order M(h)M(h)M(h) transition at 000 K from singlet to ferromagnetic at the saturation field hsh_shs​. The Haldane-DAF phase with strong F exchange in rungs and net AF exchange between rungs has continuous M(h)M(h)M(h) and is adiabatically connected to the S=1S = 1S=1 Heisenberg AF chain. The AF phase with strong F exchange in legs and net AF exchange between legs has continuous M(h)M(h)M(h) and is adiabatically connected to the spin-1/2 J1−J2J_1-J_2J1​−J2​ model with J1>0J_1 > 0J1​>0 and J2<0J_2 < 0J2​<0. All three singlet phases have finite gaps to the lowest triplet state.
The frustrated ladder with alternate ferromagnetic(F) exchange −JF-J_F−JF​ and AF exchange JAJ_AJA​ to first neighbors and F exchange −JL-J_L−JL​ to second neighbors is studied by exact diagonalization (ED) and density matrix renormalization group (DMRG) calculations in systems of 2N2N2N spins-1/2 with periodic boundary conditions. The ground state is a singlet (S=0)(S = 0)(S=0) and the singlet-triplet gap εT\varepsilon_TεT​ is finite for the exchanges considered. Spin-1/2 string correlation functions g1(N)g_1(N)g1​(N) and g2(N)g_2(N)g2​(N) are defined for an even number NNN of consecutive spins in systems with two spins per unit cell; the ladder has string order g2(∞)>0g_2(\infty)> 0g2​(∞)>0 and g1(∞)=0g_1(\infty) = 0g1​(∞)=0. The minimum N∗N^*N∗ of g2(N)g_2(N)g2​(N) is related to the range of ground-state spin correlations. Convergence to g2(∞)g_2(\infty)g2​(∞) is from below, and g1(N)g_1(N)g1​(N) decreases exponentially for N≥N∗N \geq N^*N≥N∗. Singlet valence bond (VB) diagrams account for the size dependencies. The frustrated ladder at special values of JFJ_FJF​, JLJ_LJL​ and JAJ_AJA​ reduces to well-known models such as the spin-1 Heisenberg antiferromagnet and the J1−J2J_1-J_2J1​−J2​ model, among others. Numerical analysis of ladders matches previous results for spin-1 gaps or string correlation functions and extends them to spin-1/2 systems. The nondegenerate singlet ground state of ladder is a bond-order wave, a Kekulé VB diagrams at JL=JF/2≤JAJ_L = J_F/2 \leq J_AJL​=JF​/2≤JA​, that is reversed on interchanging −JF-J_F−JF​ and JAJ_AJA​. Inversion symmetry is spontaneously broken in the dimer phase of the J1−J2J_1-J_2J1​−J2​ model where the Kekulé diagrams are the doubly degenerate ground states at J2/J1=1/2J_2/J_1 = 1/2J2​/J1​=1/2.
Abstract Ladders with 2 N spins-1/2 and singlet ( S = 0) ground states are studied numerically using exact diagonalization and density matrix renormalization group (DMRG) calculations. The curvatures E ″ ( s ) of states with the lowest energy E ( s ) at spin s = S / N ≤ 1 are obtained in the thermodynamic limit. All states have E ″ ( s ) > 0 in two phases, one with strong F exchange J F in rungs, the other with strong F exchange J L in legs. The Dimer phase with frustrated F exchanges has one or more states with E ″ ( s ) < 0. All three phases have finite gaps to the lowest triplet state. The ladder at J F → ∞ is adiabatically connected to the spin-1 Heisenberg AF chain, and at J L → ∞ to the J 1 − J 2 model.
The frustrated ladder with alternate ferromagnetic exchange $\ensuremath{-}{J}_{F}$ and antiferromagnetic exchange JA{J}_{A}JA​ to first neighbors and ferromagnetic exchange $\ensuremath{-}{J}_{L}$ to second neighbors is studied by exact diagonalization and density matrix renormalization group calculations in systems of 2N2N2N spins-12\frac{1}{2}21​ with periodic boundary conditions. The ground state is a singlet (S=0)(S=0)(S=0) and the singlet-triplet gap ${\ensuremath{\varepsilon}}_{T}$ is finite for the exchanges considered. Spin-12\frac{1}{2}21​ string correlation functions g1(N){g}_{1}(N)g1​(N) and g2(N){g}_{2}(N)g2​(N) are defined for an even number NNN of consecutive spins in systems with two spins per unit cell; the ladder has string order ${g}_{2}(\ensuremath{\infty})>0$ and ${g}_{1}(\ensuremath{\infty})=0$. The minimum N∗{N}^{*}N∗ of g2(N){g}_{2}(N)g2​(N) is related to the range of ground-state spin correlations. Convergence to ${g}_{2}(\ensuremath{\infty})$ is from below, and g1(N){g}_{1}(N)g1​(N) decreases exponentially for $N\ensuremath{\ge}{N}^{*}$. Singlet valence bond (VB) diagrams account for the size dependencies. The frustrated ladder at special values of JF,JL{J}_{F}, {J}_{L}JF​,JL​, and JA{J}_{A}JA​ reduces to well-known models such as the spin-1 Heisenberg antiferromagnet and the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model, among others. Numerical analysis of ladders matches previous results for spin-1 gaps or string correlation functions and extends them to spin-12\frac{1}{2}21​ systems. The nondegenerate singlet ground state of the ladder is a bond-order wave, a Kekul\'e VB diagram at ${J}_{L}={J}_{F}/2\ensuremath{\le}{J}_{A}$, that is reversed on interchanging $\ensuremath{-}{J}_{F}$ and JA{J}_{A}JA​. Inversion symmetry is spontaneously broken in the dimer phase of the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model where the Kekul\'e diagrams are the doubly degenerate ground states at J2/J1=1/2{J}_{2}/{J}_{1}=1/2J2​/J1​=1/2.
Abstract 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 isotropic S -type or discrete anisotropic 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 specific heat C v ( T ), magnetic susceptibility χ ( T ) and thermal entropy S ( T ) are also calculated using the transfer matrix method for various phases. The magnetic gap in the SRFM and the SLFM can be noticed from χ ( T ) and C v ( T ) curves.