Lee-Yang zeros and large-deviation statistics of a molecular zipper

Editors’ Suggestion: Phys. Rev. E 97, 012115 (2018)

The complex zeros of partition functions were originally investigated by Lee and Yang to explain the behavior of condensing gases. Since then, Lee-Yang zeros have become a powerful tool to describe phase transitions in interacting systems. Today, Lee-Yang zeros are no longer just a theoretical concept; they have been determined in recent experiments. In one approach, the Lee-Yang zeros are extracted from the high cumulants of thermodynamic observables at finite size. Here, we employ this method to investigate a phase transition in a molecular zipper. From the energy fluctuations in small zippers, we can predict the temperature at which a phase transition occurs in the thermodynamic limit. Even when the system does not undergo a sharp transition, the Lee-Yang zeros carry important information about the large-deviation statistics and its symmetry properties. Our work suggests an interesting duality between fluctuations in small systems and their phase behavior in the thermodynamic limit. These predictions may be tested in future experiments.


Show BibTeX: @article{Deger2018,
title = {{L}ee-{Y}ang zeros and large-deviation statistics of a molecular zipper},
author = {Deger, Aydin and Brandner, Kay and Flindt, Christian},
journal = {Phys. Rev. E},
volume = {97},
issue = {1},
pages = {012115},
numpages = {12},
year = {2018},
month = {Jan},
publisher = {American Physical Society},
doi = {10.1103/PhysRevE.97.012115},
url = {https://link.aps.org/doi/10.1103/PhysRevE.97.012115}}

Geometric Entanglement and Quantum Phase Transition in Generalized Cluster-XY models

Open access: Quantum Inf Process 18, 326 (2019)

In this work, we investigate quantum phase transition (QPT) in a generic family of spin chains using the ground-state energy, the energy gap and the geometric measure of entanglement (GE). In many of prior works, GE per site was used. Here, we also consider GE per block with each block size being two. This can be regarded as a coarse grain of GE per site. We introduce a useful parameterization for the family of spin chains that includes the XY models with n-site interaction, the GHZ-cluster model and a cluster antiferromagnetic model, the last of which exhibits QPT between a symmetry-protected topological (SPT) phase and a symmetry-breaking antiferromagnetic phase. As the models are exactly solvable, their ground-state wavefunctions can be obtained, and thus, their GE can be studied. It turns out that the overlap of the ground states with translationally invariant product states can be exactly calculated, and hence, the GE can be obtained via further parameter optimization. The QPTs exhibited in these models are detected by the energy gap and singular behavior of geometric entanglement. In particular, the XzY model exhibits transitions from the nontrivial SPT phase to a trivial paramagnetic phase. Moreover, the halfway XY model exhibits a first-order transition across the Barouch–McCoy circle, on which it was only a crossover in the standard XY model.


Show BibTeX: @article{Deger2019b,
author = {Deger, Aydin and Wei, Tzu-Chieh},
day = {07},
doi = {10.1007/s11128-019-2439-7},
issn = {1573-1332},
journal = {Quantum Inf. Process.},
month = {Sep},
number = {10},
pages = {326},
title = {Geometric entanglement and quantum phase transition in generalized cluster-{XY} models},
url = {https://doi.org/10.1007/s11128-019-2439-7},
volume = {18},
year = {2019},
Bdsk-Url-1 = {https://doi.org/10.1007/s11128-019-2439-7}}