arXiv subjects

Zoltán G. Soos

Publications and source records attributed to Zoltán G. Soos.

At least 19 recordsLinked to original sources

arXiv2024

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

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 $J_2/J_1 = 1/2$.

cond-mat.str-el↗

arXiv2023

Quantum Phase Transitions in Skewed Ladder Systems

In this brief review, we introduce a new spin ladder system called skewed spin ladders and discuss the exotic quantum phases of this system. The spin ladders studied are the 5/7, 3/4 and 3/5 systems corresponding to alternately fused 5 and 7 membered rings; 3 and 4 membered rings; and 3 and 5 membered rings. These ladders show completely different behaviour as the Hamiltonian model parameter is changed. When the Hamiltonian parameter is increased the 5/7 ladder switches from an initial singlet ground state to progressively higher spin ground state and then to a reentrant singlet state before finally settling to the highest spin ground state whose spin equals the number of unit cells in the system. The 3/4 ladder goes from a singlet ground state to a high spin ground state with each unit cell contributing spin 1 to the state, as the model parameter is increased. The 3/5 ladder shows a singlet ground state for small parameters and high spin ground state for intermediate values of the parameter and for still higher parameters, a reentrant singlet ground state. They can also show interesting magnetization plateaus as illustrated by studies on a specific spin ladder.

cond-mat.str-el↗

arXiv2023

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

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.

cond-mat.str-el↗

arXiv2022

Spin Peierls transition of $J_{1}-J_{2}$ and extended models with ferromagnetic $J_{1}$.Sublattice dimerization and thermodynamics of zigzag chains in $β$-TeVO$_{4}$

The spin$-1/2$ chain with ferromagnetic exchange $J_1 < 0$ between first neighbors and antiferromagnetic $J_2 > 0$ between second neighbors supports two spin-Peierls (SP) instabilities depending on the frustration $α= J_2/\vert J_1\vert$. Instead of chain dimerization with two spins per unit cell, $J_1-J_2$ models with $α> 0.65$ and linear spin-phonon coupling are unconditionally unstable to sublattice dimerization with four spins per unit cell. Unequal $J_1$ to neighbors to the right and left extends the model to gapped ($γ> 0$) chains with conditional SP transitions at $T_{SP}$ to dimerized sublattices and a weaker specific heat $C(T)$ anomaly. The spin susceptibility $χ(T)$ and $C(T)$ are obtained in the thermodynamic limit by a combination of exact diagonalization of small systems with $α> 0.65$ and density matrix renormalization group (DMRG) calculations of systems up to $N \sim 100$ spins. Both $J_1-J_2$ and $γ> 0$ models account quantitatively for $χ(T)$ and $C(T)$ in the paramagnetic phase of $β$-TeVO$_{4}$ for $T > 8$ K, but lower $T$ indicates a gapped chain instead of a $J_1-J_2$ model as previously thought. The same parameters and $T_{SP} = 4.6$ K generate a $C(T)/T$ anomaly that reproduces the anomaly at the $4.6$ K transition of $β$-TeVO$_{4}$, but not the weak $χ(T)$ signature.

cond-mat.str-el↗

arXiv2022

Density matrix renormalization group approach to the low temperature thermodynamics of correlated 1D fermionic models

The low temperature thermodynamics of correlated 1D fermionic models with spin and charge degrees of freedom is obtained by exact diagonalization (ED) of small systems and followed by density matrix renormalization group (DMRG) calculations that target the lowest hundreds of states $\{E(N)\}$ at system size $N$ instead of the ground state. Progressively larger $N$ reaches $T < 0.05t$ in correlated models with electron transfer $t$ between first neighbors and bandwidth $4t$. The size dependence of the many-fermion basis is explicitly included for arbitrary interactions by scaling the partition function. The remaining size dependence is then entirely due to the energy spectrum $\{E(N)\}$ of the model. The ED/DMRG method is applied to Hubbard and extended Hubbard models, both gapped and gapless, with $N_e = N$ or $N/2$ electrons and is validated against exact results for the magnetic susceptibility $χ(T)$ and entropy $S(T)$ per site. Some limitations of the method are noted. Special attention is given to the bond-order-wave phase of the extended Hubbard model with competing interactions and low $T$ thermodynamics sensitive to small gaps.

cond-mat.str-el↗

arXiv2021

Low temperature thermodynamics of the antiferromagnetic $J_1-J_2$ model: Entropy, critical points and spin gap

The antiferromagnetic $J_1-J_2$ model is a spin-1/2 chain with isotropic exchange $J_1 > 0$ between first neighbors and $J_2 = αJ_1$ between second neighbors. The model supports both gapless quantum phases with nondegenerate ground states and gapped phases with $Δ(α) > 0$ and doubly degenerate ground states. Exact thermodynamics is limited to $α= 0$, the linear Heisenberg antiferromagnet (HAF). Exact diagonalization of small systems at frustration $α$ followed by density matrix renormalization group (DMRG) calculations returns the entropy density $S(T,α,N)$ and magnetic susceptibility $χ(T,α,N)$ of progressively larger systems up to $N = 96$ or 152 spins. Convergence to the thermodynamics limit, $S(T,α)$ or $χ(T,α)$, is demonstrated down to $T/J \sim 0.01$ in the sectors $α< 1$ and $α> 1$. $S(T,α)$ yields the critical points between gapless phases with $S^\prime(0,α) > 0$ and gapped phases with $S^\prime(0,α) = 0$. The $S^\prime(T,α)$ maximum at $T^*(α)$ is obtained directly in chains with large $Δ(α)$ and by extrapolation for small gaps. A phenomenological approximation for $S(T,α)$ down to $T = 0$ indicates power-law deviations $T^{-γ(α)}$ from $\exp(-Δ(α)/T)$ with exponent $γ(α)$ that increases with $α$. The $χ(T,α)$ analysis also yields power-law deviations, but with exponent $η(α)$ that decreases with $α$. $S(T,α)$ and the spin density $ρ(T,α) = 4Tχ(T,α)$ probe the thermal and magnetic fluctuations, respectively, of strongly correlated spin states. Gapless chains have constant $S(T,α)/ρ(T,α)$ for $T < 0.10$. Remarkably, the ratio decreases (increases) with $T$ in chains with large (small) $Δ(α)$.

cond-mat.str-el↗

arXiv2020

Bond-bond correlations, gap relations and thermodynamics of spin-$1/2$ chains with spin-Peierls transitions and bond-order-wave phases

The spin-$1/2$ chain with antiferromagnetic exchange $J_1$ and $J_2 = αJ_1$ between first and second neighbors, respectively, has both gapless and gapped ($Δ(α) > 0$) quantum phases at frustration $0 \le α\le 3/4$. The ground state instability of regular ($δ= 0$) chains to dimerization ($δ> 0$) drives a spin-Peierls transition at $T_{SP}(α)$ that varies with $α$ in these strongly correlated systems. The thermodynamic limit of correlated states is obtained by exact treatment of short chains followed by density matrix renormalization calculations of progressively longer chains. The doubly degenerate ground states of the gapped regular phase are bond order waves (BOWs) with long-range bond-bond correlations and electronic dimerization $δ_e(α)$. The $T$ dependence of $δ_e(T,α)$ is found using four-spin correlation functions and contrasted to structural dimerization $δ(T,α)$ at $T \le T_{SP}(α)$. The relation between $T_{SP}(α)$ and the $T = 0$ gap $Δ(δ(0),α)$ varies with frustration in both gapless and gapped phases. The magnetic susceptibility $χ(T,α)$ at $T > T_{SP}$ can be used to identify physical realizations of spin-Peierls systems. The $α= 1/2$ chain illustrates the characteristic BOW features of a regular chain with a large singlet-triplet gap and electronic dimerization.

cond-mat.str-el↗

arXiv2020

Modeling the spin-Peierls transition of spin-$1/2$ chains with correlated states: $J_1-J_2$ model, CuGeO$_3$ and TTF-CuS$_4$C$_4$(CF$_3$)$_4$

The spin-Peierls transition at $T_{SP}$ of spin-$1/2$ chains with isotropic exchange interactions has previously been modeled as correlated for $T > T_{SP}$ and mean field for $T < T_{SP}$. We use correlated states throughout in the $J_1-J_2$ model with antiferromagnetic exchange $J_1$ and $J_2 = αJ_1$ between first and second neighbors, respectively, and variable frustration $0 \leq α\leq 0.50$. The thermodynamic limit is reached at high $T$ by exact diagonalization of short chains and at low $T$ by density matrix renormalization group calculations of progressively longer chains. In contrast to mean field results, correlated states of 1D models with linear spin-phonon coupling and a harmonic adiabatic lattice provide an internally consistent description in which the parameter $T_{SP}$ yields both the stiffness and the lattice dimerization $δ(T)$. The relation between $T_{SP}$ and $Δ(δ,α)$, the $T = 0$ gap induced by dimerization, depends strongly on $α$ and deviates from the BCS gap relation that holds in uncorrelated spin chains. Correlated states account quantitatively for the magnetic susceptibility of TTF-CuS$_4$C$_4$(CF$_3$)$_4$ crystals ($J_1 = 79$ K, $α= 0$, $T_{SP} = 12$ K) and CuGeO$_3$ crystals ($J_1 = 160$ K, $α= 0.35$, $T_{SP} = 14$ K). The same parameters describe the specific heat anomaly of CuGeO$_3$ and inelastic neutron scattering. Modeling the spin-Peierls transition with correlated states exploits the fact that $δ(0)$ limits the range of spin correlations at $T = 0$ while $T > 0$ limits the range at $δ= 0$.

cond-mat.str-el↗

arXiv2019

Spin-Peierls transition of the dimer phase of the $J_1-J_2$ model: Energy cusp and CuGeO$_3$ thermodynamics

The spin-Peierls transition is modeled in the dimer phase of the spin-$1/2$ chain with exchanges $J_1$, $J_2 = αJ_1$ between first and second neighbors. The degenerate ground state generates an energy cusp that qualitatively changes the dimerization $δ(T)$ compared to Peierls systems with nondegenerate ground states. The parameters $J_1 = 160$ K, $α= 0.35$ plus a lattice stiffness account for the magnetic susceptibility of CuGeO$_3$, its specific heat anomaly, and the $T$ dependence of the lowest gap.

cond-mat.str-el↗

arXiv2019

Hybrid ED/DMRG approach to the thermodynamics of 1D quantum models

Exact diagonalization (ED) of small model systems gives the thermodynamics of spin chains or quantum cell models at high temperature $T$. Density matrix renormalization group (DMRG) calculations of progressively larger systems are used to obtain excitations up to a cutoff $W_C$ and the low-$T$ thermodynamics. The hybrid approach is applied to the magnetic susceptibility $χ(T)$ and specific heat $C(T)$ of spin-$1/2$ chains with isotropic exchange such as the linear Heisenberg antiferromagnet (HAF) and the frustrated $J_1-J_2$ model with ferromagnetic (F) $J_1 < 0$ and antiferromagnetic (AF) $J_2 > 0$. The hybrid approach is fully validated by comparison with HAF results. It extends $J_1-J_2$ thermodynamics down to $T \sim 0.01|J_1|$ for $J_2/|J_1| \geq α_c = 1/4$ and is consistent with other methods. The criterion for the cutoff $W_C(N)$ in systems of $N$ spins is discussed. The cutoff leads to bounds for the thermodynamic limit that are best satisfied at a specific $T(N)$ at system size $N$.

cond-mat.str-el↗

arXiv2018

Spin-specific heat determination of the ratio of competing first- and second-neighbor exchange interactions in frustrated spin-$\frac{1}{2}$ chains

The magnetic susceptibility $χ(T)$ of spin-1/2 chains is widely used to quantify exchange interactions, even though $χ(T)$ is similar for different combinations of ferromagnetic $J_1$ between first neighbors and antiferromagnetic $J_2$ between second neighbors. We point out that the spin specific heat $C(T)$ directly determines the ratio $α= J_2/|J_1|$ of competing interactions. The $J_1-J_2$ model is used to fit the isothermal magnetization $M(T,H)$ and $C(T,H)$ of spin-1/2 Cu(II) chains in LiCuSbO$_4$. By fixing $α$, $C(T)$ resolves the offsetting $J_1$, $α$ combinations obtained from $M(T,H)$ in cuprates with frustrated spin chains.

cond-mat.str-el↗

arXiv2017

Quantum phases of frustrated 2-leg spin-1/2 ladders with skewed rungs

The quantum phases of 2-leg spin-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 $J_1 \gg J_2$. Ladders with skewed rungs and variable $J_1$ have frustrated AF interactions leading to multiple quantum phases: AF at small $J_1$, either F or AF at large $J_1$, as well as bond-order-wave phases or reentrant AF (singlet) phases at intermediate $J_1$.

cond-mat.str-el↗

arXiv2016

Density matrix renormalization group (DMRG) for cyclic and centrosymmetric linear chains

The density matrix renormalization group (DMRG) method generates the low-energy states of linear systems of $N$ sites with a few degrees of freedom at each site by starting with a small system and adding sites step by step while keeping constant the dimension of the truncated Hilbert space. DMRG algorithms are adapted to open chains with inversion symmetry at the central site, to cyclic chains and to weakly coupled chains. Physical properties rather than energy accuracy is the motivation. The algorithms are applied to the edge states of linear Heisenberg antiferromagnets with spin $S \ge 1$ and to the quantum phases of a frustrated spin-1/2 chain with exchange between first and second neighbors. The algorithms are found to be accurate for extended Hubbard and related 1D models with charge and spin degrees of freedom.

cond-mat.str-el↗

arXiv2016

Boundary-induced spin density waves in linear Heisenberg antiferromagnetic spin chains with $\mathbf{S \ge 1}$

Linear Heisenberg antiferromagnets (HAFs) are chains of spin-$S$ sites with isotropic exchange $J$ between neighbors. Open and periodic boundary conditions return the same ground state energy in the thermodynamic limit, but not the same spin $S_G$ when $S \ge 1$. The ground state of open chains of N spins has $S_G = 0$ or $S$, respectively, for even or odd N. Density matrix renormalization group (DMRG) calculations with different algorithms for even and odd N are presented up to N = 500 for the energy and spin densities $ρ(r,N)$ of edge states in HAFs with $S = 1$, 3/2 and 2. The edge states are boundary-induced spin density waves (BI-SDWs) with $ρ(r,N)\propto(-1)^{r-1}$ for $r=1,2,\ldots N$. The SDWs are in phase when N is odd, out of phase when N is even, and have finite excitation energy $Γ(N)$ that decreases exponentially with N for integer $S$ and faster than 1/N for half integer $S$. The spin densities and excitation energy are quantitatively modeled for integer $S$ chains longer than $5 ξ$ spins by two parameters, the correlation length $ξ$ and the SDW amplitude, with $ξ= 6.048$ for $S = 1$ and 49.0 for $S = 2$. The BI-SDWs of $S = 3/2$ chains are not localized and are qualitatively different for even and odd N. Exchange between the ends for odd N is mediated by a delocalized effective spin in the middle that increases $|Γ(N)|$ and weakens the size dependence. The nonlinear sigma model (NL$σ$M) has been applied the HAFs, primarily to $S = 1$ with even N, to discuss spin densities and exchange between localized states at the ends as $Γ(N) \propto (-1)^N \exp(-N/ξ)$...

cond-mat.str-el↗

arXiv2016

Numerical study of incommensurate and decoupled phases of spin-1/2 chains with isotropic exchange J1, J2 between first and second neighbors

The spin-1/2 chain with isotropic exchange J1, J2 > 0 between first and second neighbors is frustrated for either sign of J1 and has a singlet ground state (GS) for J1/J2 $\ge - 4$. Its rich quantum phase diagram supports gapless, gapped, commensurate (C), incommensurate (IC) and other phases. Critical points J1/J2 are evaluated using exact diagonalization (ED) and density matrix renormalization group (DMRG) calculations. The wave vector $q_G$ of spin correlations is related to GS degeneracy and obtained as the peak of the spin structure factor $S(q)$. Variable $q_G$ indicates IC phases in two $J1/J2$ intervals, [ -4, -1.24] and [0.44, 2], and a C-IC point at J1/J2 = 2. The decoupled C phase in [-1.24, 0.44] has constant $q_G = π/2$, nondegenerate GS, and a lowest triplet state with broken spin density on sublattices of odd and even numbered sites. The lowest triplet and singlet excitations, $E_m$ and $E_σ$, are degenerate in finite systems at specific frustration $J1/J2$. Level crossing extrapolates in the thermodynamic limit to the same critical points as $q_G$. The $S(q)$ peak diverges at $q_G = π$ in the gapless phase with $J1/J2 > 4.148$ and quasi-long-range order (QLRO({$π$})). $S(q)$ diverges at $\pm π/2$ in the decoupled phase with QLRO({$π$}/2), but is finite in gapped phases with finite range correlations. Numerical results and field theory agree at small $J2/J1$ but disagree for the decoupled phase with weak exchange $J1$ between sublattices. Two related models are summarized: one has an exact gapless decoupled phase with QLRO({$π$}/2) and no IC phases; the other has a single IC phase without a decoupled phase in between.

cond-mat.str-el↗

arXiv2015

Level crossing, spin structure factor and quantum phases of the frustrated spin-1/2 chain with first and second neighbor exchange

The spin-1/2 chain with isotropic Heisenberg exchange $J_1$, $J_2 > 0$ between first and second neighbors is frustrated for either sign of J1. Its quantum phase diagram has critical points at fixed $J_1/J_2$ between gapless phases with nondegenerate ground state (GS) and quasi-long-range order (QLRO) and gapped phases with doubly degenerate GS and spin correlation functions of finite range. In finite chains, exact diagonalization (ED) estimates critical points as level crossing of excited states. GS spin correlations enter in the spin structure factor $S(q)$ that diverges at wave vector $q_m$ in QLRO($q_m$) phases with periodicity $2π/q_m$ but remains finite in gapped phases. $S(q_m)$ is evaluated using ED and density matrix renormalization group (DMRG) calculations. Level crossing and the magnitude of $S(q_m)$ are independent and complementary probes of quantum phases, based respectively on excited and ground states. Both indicate a gapless QLRO($π/2$) phase between $-1.2 < J_1/|J_2| < 0.45$. Numerical results and field theory agree well for quantum critical points at small frustration $J_2$ but disagree in the sector of weak exchange $J_1$ between Heisenberg antiferromagnetic chains on sublattices of odd and even-numbered sites.

cond-mat.str-el↗

arXiv2012

Spin parity and broken symmetry in finite spin-1/2 chains with frustrated exchange: quantum transition from high to low spin

Exact diagonalization of finite spin-1/2 chains with periodic boundary conditions is applied to the ground state (gs) of chains with ferromagnetic (F) exchange $J_1 < 0$between first neighbors, antiferromagnetic (AF) exchange $J_2 = αJ_1 > 0$between second neighbors, and axial anisotropy $0 \le Δ\le 1$. In zero field, the gs is in the $S_z = 0$ sector for the relevant parameters and is doubly degenerate at multiple points $γ_m = (α_m, Δ_m)$ in the $α$, $Δ$ plane. Degeneracy under inversion at sites or spin parity or both leads, respectively, to a bond order wave (BOW), to staggered magnetization or to vector chiral (VC) order. Exact results up to $N = 28$ spins directly yield order parameters and spin correlation functions whose weak N dependencies allow inferences about infinite chains. The high-spin gs at $J_2 = 0$ changes discontinuously at $γ_1 = (-1/4, 1)$ to a singlet in the isotropic ($Δ= 1$) chain. The transition from high to low spin $S(α, Δ)$ is continuous for $ Δ< Δ_B = 0.95 \pm 0.01$ on the degeneracy line $α_1(Δ)$. The gs has staggered magnetization between $Δ_A = 0.72$ and $Δ_B$, and a BOW for $Δ< Δ_A$. When both inversion and spin parity are reversed at $γ_m$, the correlation functions $C(p)$ for spins separated by $p$ sites are identical. $C(p)$ minima are shifted by $π/2$ from the minima of VC order parameters at separation $p$, consistent with right and left-handed helices along the z axis and spins in the xy plane. Degenerate gs of finite chains are related to quantum phase diagrams of extended $α$, $Δ$ chains, with good agreement for order parameters along the line $α_1(Δ)$.

cond-mat.str-el↗

arXiv2011

Surface dipole of F4TCNQ films: Collective charge transfer and dipole-dipole repulsion in submonolayers

A charge transfer (CT) model is introduced for strong acceptors like A = F4TCNQ that are ionized on surfaces at low coverage θ. Each A forms a CT dimer with a surface state S. Dipole-dipole repulsion grows as θ^(3/2) up to θ = 1 in a full monolayer. Electron transfer ρ(θ) within dimers is found self-consistently and decreases with increasing coverage. The surface dipole and work function shift ΔΦ are proportional to θρ(θ). The CT model has implications for photoemission and accounts for ΔΦ(d) profiles of F4TCNQ films of thickness d on Cu(1,1,1) or on hydrogenated diamond (1,0,0). The CT model also describes ΔΦ(θ) of organic donors on metals and is contrasted to previous treatments of dipoles on a surface.

cond-mat.mtrl-sci↗