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arXiv:2012.07486 · Physical review. B./Physical review. B

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

Sambunath Das, Dayasindhu Dey, Manoranjan Kumar, S. Ramasesha

Published Sep 27, 2021• 4 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.104.125138

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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 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 ${J}_{1}\ensuremath{\gg}{J}_{2}$. 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​.
We study the quantum phase transitions of frustrated antiferromagnetic Heisenberg spin-1 systems on the 3/4 and 3/5 skewed two leg ladder geometries. These systems can be viewed as arising by periodically removing rung bonds from a zigzag ladder. We find that in large systems, the ground state (gs) of the 3/4 ladder switches from a singlet to a magnetic state for J1≥1.82; the gs spin corresponds to the ferromagnetic alignment of effective S=2 objects on each unit cell. The gs of antiferromagnetic exchange Heisenberg spin-1 system on a 3/5 skewed ladder is highly frustrated and has spiral spin arrangements. The amplitude of the spin density wave in the 3/5 ladder is significantly larger compared to that in the magnetic state of the 3/4 ladder. The gs of the system switches between singlet state and low spin magnetic states multiple times on tuning J1 in a finite size system. The switching pattern is nonmonotonic as a function of J1 and depends on the system size. It appears to be the consequence of a higher J1 favoring a higher spin magnetic state and the finite system favoring a standing spin wave. For some specific parameter values, the magnetic gs in the 3/5 system is doubly degenerate in two different mirror symmetry subspaces. This degeneracy leads to spontaneous spin-parity and mirror symmetry breaking, giving rise to spin current in the gs of the system.
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.
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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 SSS or σσσ-type spins) are aligned in the same direction. Whereas, in anisotropic antiferromagnetic phase, both SSS and σσσ-type of spins are anti-ferromagnetically aligned with each other, two nearest SSS spins along the rung form an anisotropic singlet bond whereas two nearest σσσ 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)Cv(T)Cv(T), χ(T)χ(T)χ(T) and S(T)S(T)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)χ(T)χ(T) and Cv(T)Cv(T)Cv(T) curves.
Abstract In this work, we consider a frustrated two‐leg spin‐1/2 ladder composed of Heisenberg ferromagnetic and antiferromagnetic spin‐1/2 chains, and nearest spins from different legs interact via Heisenberg type rung exchange interactions that can be either ferromagnetic or antiferromagnetic in nature. The competing exchange interactions in the system lead to five different quantum phases like ferromagnetic, non‐collinear ferrimagnetic (NCF), , antiferromagnetic and dimer phases. The quantum phase diagram is constructed for the Heisenberg spin‐1/2 model and the phases are characterized using the correlation functions which are calculated by the density matrix renormalization group method. We also analyze the stability of phase and calculate the pitch angle in the NCF phase.