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Journal of Physics Condensed Matter

The gapless energy spectrum and spin-Peierls instability of 1D Heisenberg spin systems in polymeric complexes of transition metals and hypothetical carbon allotropes

Vladyslav O. Cheranovskii, Victor V. Slavin, Andrei L. Tchougréeff, Richard Dronskowski

Published Apr 15, 2019• 8 citations
Publisher

Abstract

We investigate the spin-Peierls instability of some periodic 1D Heisenberg spin systems having a gapless energy spectrum at different values of coupling J between the unit cells. Using the density-matrix renormalization group method we numerically study the dependence of critical exponents p of spin-Peierls transition of above spin systems on the value of J. In contrast to chain systems, we find significantly non-monotonous dependence p (J) for three-legs ladder system. In the limit of weak coupling J we derive effective spin s chain Hamiltonians describing the low-energy states of the system considered by means of perturbation theory. The value of site spin s coincides with the value of the ground-state spin of the isolated unit cell of the system considered. This means that at small J values all the systems with the singlet ground state and the same half-integer value of s should have a similar critical behavior which is in agreement with our numerical study. The presence of gapped excitations inside the unit cells at small values of J should give, for our spin systems, at least one intermediate plateau in field dependence of magnetization at low temperatures. The stability of this plateau against the increase of the values of J and temperature is studied using the quantum Monte-Carlo method.

DOI
10.1088/1361-648x/ab197a

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We investigate the spin-Peierls instability of some periodic 1D Heisenberg spin systems having a gapless energy spectrum at different values of coupling J between the unit cells. Using the density-matrix renormalization group method we numerically study the dependence of critical exponents p of spin-Peierls transition of above spin systems on the value of J. In contrast to chain systems, we find significantly non-monotonous dependence p (J) for three-legs ladder system. In the limit of weak coupling J we derive effective spin s chain Hamiltonians describing the low-energy states of the system considered by means of perturbation theory. The value of site spin s coincides with the value of the ground-state spin of the isolated unit cell of the system considered. This means that at small J values all the systems with the singlet ground state and the same half-integer value of s should have a similar critical behavior which is in agreement with our numerical study. The presence of gapped excitations inside the unit cells at small values of J should give, for our spin systems, at least one intermediate plateau in field dependence of magnetization at low temperatures. The stability of this plateau against the increase of the values of J and temperature is studied using the quantum Monte-Carlo method.
A class of frustrated one-dimensional periodic Heisenberg spin systems formed either by triangular unit cells with spin 1/2 or by composite unit cells formed by two different structural units, triangles and small linear segments formed by an odd number of spin-1/2 is investigated. Based on perturbative processing and numerical calculations of the density matrix renormalization group method, the gapless character of the exact energy spectrum of excitation for these systems was found. Their instability with respect to regular (Peierls) oscillations of interactions between structural units is demonstrated. The corresponding critical exponents for the energies of the ground state are estimated numerically. For some frustrated systems, a quantum phase transition associated with the spin symmetry of the ground state, caused by frustration, has been discovered.
Abstract Focusing on novel highly correlated low‐dimensional systems, we investigate a class of quasione‐dimensional systems with an even number of spin‐½ sites per unit cell, for which we find, here, that it does not give a gap in the exact excitation spectrum. The unit cells of these systems are formed by two different structural units, each with an odd number of sites. We find the instability of these systems against the regular oscillations of the interactions between structural units and estimate numerically the corresponding critical exponents for the ground‐state energies. In contrast to the well‐known spin‐Peierls instability, this type of structural instability does not change the symmetry of the above systems. We also present a class of disordered one‐dimensional spin systems formed by different types of structural units with odd numbers of spins to demonstrate a critical behavior similar to a homogeneous spin‐½ chain in the limit of weak interactions between structural units.
Because the three-leg ladder behaves like a renormalized single Heisenberg chain, we argue that a spin-Peierls instability must occur in this system when it is coupled to three-dimensional phonons. Using the bond-mean-field theory, we show that this is indeed the case. The dimerized state below the spin-Peierls transition temperature forms into the columnar dimerized phase instead of the staggered one. This contrasts with the argument based on antiferromagnetism. A physical argument based rather on spin bonding into singlets could explain why the columnar configuration is favored. No quantum criticality (gaplessness) can occur in the columnar arrangement of the dimerized chains.
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.
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 spin-Peierls (SP) transition of one-dimensional chain polymeric complexes coupled to lattice by means of many-body Green's function theory. The chain effective elastic constant is an intrinsic factor that determines the order of SP transition. It is found that the SP transition temperature T(SP) and the susceptibility-maximum temperature T(max) are in agreement with the experimental results. When an external magnetic field is applied to the chain, it makes T(SP) and T(max) decrease, and drives the SP transition from the second order to the first order. Besides, we show that the two-site thermal entanglement entropy is a good indicator of SP transition. Further considering the effect of interchain coupling on SP transition, with weak coupling of double-chain, the theoretical values are closer to the experimental results. We also calculate the density of states and spectral functions, which show that the energy gap vanishes at a critical temperature lower than T(SP), indicating a gapless SP phase lies in the gapped dimerized phase. The interchain coupling can drive the SP transition from the second order to the first order, while the SP dimerization may collapse for large interchain couplings.