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Thermodynamic Phase Transitions in Finite Su-Schrieffer-Heeger Chains: Metastability and Heat Capacity Anomalies

Carlos Magno da Conceição, Julio César Pérez-Pedraza, Alfredo Raya, Cristian Villavicencio

Abstract

We investigate the thermodynamic properties of finite Su-Schrieffer-Heeger (SSH) chains in thermal equilibrium at fixed temperature and chemical potential. Using the canonical and grand canonical ensembles, we calculate the energy density, particle number density, entropy, and heat capacity as functions of temperature, chemical potential, and hopping asymmetry. Our analysis reveals the emergence of a metastable thermodynamic phase characterized by a local minimum in the heat capacity for non-dimerized configurations, signaling a second-order phase transition distinct from the topological phase transition. This metastable phase becomes more pronounced as the hopping asymmetry increases and the chain length grows. We demonstrate that while the topological properties are determined by boundary states, the bulk thermodynamic behavior exhibits rich phase structure that can be tuned through the hopping parameter ratio. These findings provide insights into the interplay between topology, finite-size effects, and thermal fluctuations in one-dimensional topological systems, with potential implications for experimental realizations in cold atoms, photonic systems, and topoelectrical circuits.

Thermodynamic Phase Transitions in Finite Su-Schrieffer-Heeger Chains: Metastability and Heat Capacity Anomalies

Abstract

We investigate the thermodynamic properties of finite Su-Schrieffer-Heeger (SSH) chains in thermal equilibrium at fixed temperature and chemical potential. Using the canonical and grand canonical ensembles, we calculate the energy density, particle number density, entropy, and heat capacity as functions of temperature, chemical potential, and hopping asymmetry. Our analysis reveals the emergence of a metastable thermodynamic phase characterized by a local minimum in the heat capacity for non-dimerized configurations, signaling a second-order phase transition distinct from the topological phase transition. This metastable phase becomes more pronounced as the hopping asymmetry increases and the chain length grows. We demonstrate that while the topological properties are determined by boundary states, the bulk thermodynamic behavior exhibits rich phase structure that can be tuned through the hopping parameter ratio. These findings provide insights into the interplay between topology, finite-size effects, and thermal fluctuations in one-dimensional topological systems, with potential implications for experimental realizations in cold atoms, photonic systems, and topoelectrical circuits.
Paper Structure (22 sections, 20 equations, 5 figures)

This paper contains 22 sections, 20 equations, 5 figures.

Table of Contents

  1. Introduction
  2. The Model
  3. Hamiltonian and Wannier states
  4. Energy eigenvalues and eigenstates
  5. Boundary conditions and energy spectrum
  6. Parametrization and energy spectrum
  7. Thermodynamics
  8. Grand canonical ensemble and partition function
  9. Thermodynamic quantities
  10. Heat capacity
  11. Dimensionless quantities and parameter space
  12. Results and Discussion
  13. Fixed chain length: Open boundary conditions
  14. Heat capacity landscape
  15. Temperature slices and density correlations
  16. ...and 7 more sections

Figures (5)

  • Figure 1: Illustration of the crystal structure in our model of a fully dimerized finite chain of atoms with $N+1$ sites. Hopping parameters are shown as thick and thin lines.
  • Figure 2: Heat capacity landscape. Upper panel: Varying the number of sites $N$ with a fixed hopping angle value $\theta = \pi/8$. Lower panel: Varying the values for the hopping angle $\theta$, with a fixed number of sites $N=20$.
  • Figure 3: Temperature dependence of relevant quantities for fixed values of the number of sites $N=20$ and chemical potential $\mu=1.0 \epsilon$. Upper panel: Mean energy and mean number of particles. Lower panel: Heat capacity of the system.
  • Figure 4: Heat capacity of the system as a function of temperature for a fixed mean number of particles. Left panel:$\bar{N}=20$. Right panel:$\bar{N}=80$. In both graphs the number of sites $N=40$ is kept fixed.
  • Figure 5: Energy density as a function of temperature for different values of the parameter $\theta$ for a fixed mean number of particles. Left panel:$\bar{N}=20$. Right panel:$\bar{N}=80$. In both graphs, the number of sites $N=40$ is kept fixed. Insets show the behavior of the chemical potential with the temperature in each case.