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Low Temperature Physics

The energy spectrum and low-temperature magnetic properties of the decorated two-leg mixed spin ladder

Vladyslav O. Cheranovskii, E. V. Ezerskaya, A. O. Kabatova

Published Apr 1, 2023• 3 citations
Publisher

Abstract

The energy spectra and low-temperature magnetic properties of two one-dimensional Heisenberg mixed spin (s = 1, 1/2) systems, namely decorated two-leg mixed spin ladders with the lattice topology of polyacene, are studied. The gapless character of the exact excitation energy spectra for both ladder models has been determined. We found numerically that the model with macroscopic ground state spin S0 has gapped excitations with the spin S > S0. This leads to the appearance of an intermediate plateau in field dependence of magnetization at low temperatures. We have shown that the ladder with equal coupling in legs has the maximal size of this plateau at the same coupling in rungs. For a mixed spin ladder model with Ising interactions in legs, the appearance of two intermediate magnetization plateaus at low temperatures and some values of coupling parameters was shown.

DOI
10.1063/10.0017584

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The energy spectra and low-temperature magnetic properties of two one-dimensional Heisenberg mixed spin (s = 1, 1/2) systems, namely decorated two-leg mixed spin ladders with the lattice topology of polyacene, are studied. The gapless character of the exact excitation energy spectra for both ladder models has been determined. We found numerically that the model with macroscopic ground state spin S0 has gapped excitations with the spin S > S0. This leads to the appearance of an intermediate plateau in field dependence of magnetization at low temperatures. We have shown that the ladder with equal coupling in legs has the maximal size of this plateau at the same coupling in rungs. For a mixed spin ladder model with Ising interactions in legs, the appearance of two intermediate magnetization plateaus at low temperatures and some values of coupling parameters was shown.
The peculiarities of the energy spectrum of the decorated mixed spin two-leg ladder system having three spin unit cells have been studied by the perturbation theory in the limit of dominant spin coupling in ladder rungs. It is shown, that despite the singlet ground state, this spin ladder may have an intermediate plateau in a low-temperature magnetization profile. The existence of a similar plateau was shown also in the case of some intermediate values of coupling parameters by means of exact diagonalization study of small ladder clusters and by the density-matrix renormalization group calculations. We also found that the Ising type of interactions in ladder rungs may lead to the disappearance of the above intermediate magnetization plateau for the corresponding isotropic spin ladder.
Using the density-matrix renormalization-group technique we investigate the low-energy properties and the magnetization-plateau behavior in a two-leg mixed spin ladder consisting of a spin-1/2 chain coupled with a spin-1 chain. The calculated results show that the system is in the same universality class as the spin-3/2 chain when the interchain coupling is strongly ferromagnetic, but the similarity between the two systems is less clear under other coupling conditions. We have identified two types of magnetization-plateau phases. The calculation of the magnetization distribution on the spin-1/2 and the spin-1 chains on the ladder shows that one plateau phase is related to the partially magnetized valence-bond-solid state, and the other plateau state contains strongly coupled S=1S=1S=1 and s=1/2s=1/2s=1/2 spins on the rung.
The experimental realization of various spin ladder systems has prompted their detailed theoretical investigations. Here we study the evolution of ground-state magnetization with an external magnetic field for two different antiferromagnetic systems: a three-legged spin-1/21/21/2 ladder, and a two-legged spin-1/21/21/2 ladder with an additional diagonal interaction. The finite system density-matrix renormalization-group method is employed for numerical studies of the three-chain system, and an effective low-energy Hamiltonian is used in the limit of strong interchain coupling to study the two- and three-chain systems. The three-chain system has a magnetization plateau at one-third of the saturation magnetization. The two-chain system has a plateau at zero magnetization due to a gap above the singlet ground state. It also has a plateau at half of the saturation magnetization for a certain range of values of the couplings. We study the regions of transitions between plateaus numerically and analytically, and find that they are described, at first order in a strong-coupling expansion, by an XXZ\mathrm{XXZ}XXZ spin-1/21/21/2 chain in a magnetic field; the second-order terms give corrections to the XXZ\mathrm{XXZ}XXZ model. We also study numerically some low-temperature properties of the three-chain system, such as the magnetization, magnetic susceptibility and specific heat.
At zero temperature, thermal fluctuation is eliminated and phase transitions will occur due to quantum fluctuations that arise from the Heisenberg uncertainty principle. Magnetic insulators, described by the Heisenberg model Hamiltonian, are a known class of physical systems that can undergo quantum phase transitions when submitted to a magnetic field. The magnetic field induces the transition by closing energy gaps through the Zeeman effect. Examples of systems that undergo these transitions are the antiferromagnetic spin-1 chain, the antiferromagnetic spin- 1/2 ladder, the ferrimagnetic mixed spin-1 and spin- 1/2 chains and ladders. The presence of a gap in the energy spectrum with zero magnetic field leads to a magnetization plateau in the magnetization curve. We use the density matrix renormalization group to investigate the magnetization curves of the mixed spin-1 and spin- 1/2 ladder, for antiferromagnetic and ferro- magnetic couplings between the ladder legs J⊥. For J⊥ > 0, the ground-state is ferrimagnetic with the total spin equal to 1/3 of the saturation value, in accord with the Lieb-Mattis theorem. The magnetization curve presents a plateau at total magnetization 1/3 of the saturation value, the 1/3-plateau since the ground state has a gap to excitations that increase the total spin by 1 unit. Decreasing J⊥ below zero, the ground state becomes a singlet, but the 1/3-plateau survives down to a critical value J⊥ = Jc. Given that the gap closes with the magnetization fixed, it is a Kosterlitz-Thouless transition type. To determine Jc, we have made a finite-size scale analysis of the plateau width.
We study the low-lying excitations and thermodynamic properties of a ferrimagnetic Heisenberg two-leg ladder, which is composed of alternating-spin (1/2, 1) double chains with antiferromagnetic coupling between the chains. The spin excitation spectra as well as the corresponding energy gaps are calculated by means of the Schwinger-boson mean-field theory. The two interactions between the chains and along the chains play an important role in determining the two branches of the spectrum, not only regarding the size of the low-lying excitation energy gap but also the bandgap between the optical spectrum and the acoustic spectrum. In addition, the two energy gaps and the specific heat have also been calculated at low temperatures.
The magnetic and thermodynamic properties of a ferrimagnetic decorated spin-(12,1)(\frac{1}{2},1)(21​,1) Heisenberg chain with spin-1 pendant spins are investigated for three cases: (A) J1,J2>0{J}_{1},{J}_{2}>0J1​,J2​>0; (B) J1>0{J}_{1}>0J1​>0 and J2<0{J}_{2}<0J2​<0; and (C) J1<0{J}_{1}<0J1​<0 and J2>0{J}_{2}>0J2​>0, where J1{J}_{1}J1​ and J2{J}_{2}J2​ are the exchange couplings between spins in the chain and along the rung, respectively. The low-lying and magnetic properties are explored jointly by the real-space renormalization group, spin wave, and density-matrix renormalization-group methods, while the transfer-matrix renormalization-group method is invoked to study the thermodynamics. It is found that the magnon spectra consist of a gapless and two gapped branches. Two branches in case (C) have intersections. The coupling dependence of low-energy gaps are analyzed. In a magnetic field, a m=32m=\frac{3}{2}m=23​ (mmm is the magnetization per unit cell) plateau is observed for case (A), while two plateaux at m=12m=\frac{1}{2}m=21​ and 32\frac{3}{2}23​ are observed for cases (B) and (C). Between the two plateaux in cases (B) and (C), the sublattice magnetizations for the spins coupled by ferromagnetic interactions have decreasing regions with increasing the magnetic field. At finite temperature, the zero-field susceptibility temperature product $\ensuremath{\chi}T$ and specific heat exhibit distinct exotic features with varying the couplings and temperature for different cases. $\ensuremath{\chi}T$ is found to converge as $T\ensuremath{\rightarrow}0$, which is different from the divergent behavior in the spin-(12,1)(\frac{1}{2},1)(21​,1) mixed-spin chain without pendants. The observed thermodynamic behaviors are also discussed with the help of their low-lying excitations.