Lee-Yang theory of the two-dimensional quantum Ising model

M., Vecsei, Pascal; Lado, José L.; Flindt, Christian

doi:10.1103/physrevb.106.054402

Cited by 8 publications

(8 citation statements)

References 74 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Lee-Yang theory of phase transitions has found applications in condensed matter physics [37,40,41,[44][45][46], atomic physics [38] and particle physics [39,42,43,47,[69][70][71][72]. Recently, it has been extended to the zeros of the moment generating function that describes the fluctuations of the order parameter [57,58] and thereby allows for the detection of quantum phase transitions. Following this approach, we define the moment generating function…”

Section: Lee-yang Theorymentioning

confidence: 99%

“…To determine the position of the zeros that are closest to s = 0, we use the cumulant method that was developed in Refs. [40,52,53,57,58]. In this approach, the zeros of the moment generating function can be determined from the high cumulants of the order parameter.…”

Section: Lee-yang Theorymentioning

confidence: 99%

“…In this approach, the zeros of the moment generating function can be determined from the high cumulants of the order parameter. By doing so for different system sizes, we can then find the convergence points in the thermodynamic limit using finite-size scaling [40,52,57,58]. The cumulant method allows us to express the zeros in terms of the high cumulants of the magnetization.…”

Section: Lee-yang Theorymentioning

confidence: 99%

“…Lee-Yang zeros are not just a theoretical concept, but they can also be determined experimentally [49][50][51][52][53]. In recent years, applications of Lee-Yang theory have been expanded to dynamical quantum phase transitions in quantum many-body systems after a quench [54][55][56] and to quantum phase transitions in systems at zero temperature [57,58].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Lee-Yang theory of quantum phase transitions with neural network quantum states

M.¹,

Flindt²,

Lado³

2023

Preprint

View full text Add to dashboard Cite

Predicting the phase diagram of interacting quantum many-body systems is a central problem in condensed matter physics and related fields. A variety of quantum many-body systems, ranging from unconventional superconductors to spin liquids, exhibit complex competing phases whose theoretical description has been the focus of intense efforts. Here, we show that neural network quantum states can be combined with a Lee-Yang theory of quantum phase transitions to predict the critical points of strongly-correlated spin lattices. Specifically, we implement our approach for quantum phase transitions in the transverse-field Ising model on different lattice geometries in one, two, and three dimensions. We show that the Lee-Yang theory combined with neural network quantum states yields predictions of the critical field, which are consistent with large-scale quantum many-body methods. As such, our results provide a starting point for determining the phase diagram of more complex quantum many-body systems, including frustrated Heisenberg and Hubbard models.

show abstract

Section: Lee-yang Theorymentioning

confidence: 99%

Section: Lee-yang Theorymentioning

confidence: 99%

Section: Lee-yang Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Lee-Yang theory of quantum phase transitions with neural network quantum states

M.¹,

Flindt²,

Lado³

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…The framework is not restricted to equilibrium settings, but can also be applied to non-equilibrium phase transitions [39,45]. In addition, it has recently been extended to the quantum realm to describe quantum phase transitions in the ground state of interacting quantum manybody systems [46][47][48] and to dynamical quantum phase transitions in spin lattices following a quench [49,50].…”

Section: Introductionmentioning

confidence: 99%

Lee-Yang theory of Bose-Einstein condensation

Brange¹,

Pyhäranta²,

Brandner³

et al. 2023

Preprint

View full text Add to dashboard Cite

Bose-Einstein condensation happens as a gas of bosons is cooled below its transition temperature, and the ground state becomes macroscopically occupied. The phase transition occurs in the thermodynamic limit of many particles. However, recent experimental progress has made it possible to assemble quantum many-body systems from bottom up, for example, by adding single atoms to an optical lattice one at a time. Here, we show how one can predict the condensation temperature of a Bose gas from the energy fluctuations of a small number of bosons. To this end, we make use of recent advances in Lee-Yang theories of phase transitions, which allow us to determine the zeros and the poles of the partition function in the complex plane of the inverse temperature from the high cumulants of the energy fluctuations. By increasing the number of bosons in the trapping potential, we can predict the convergence point of the partition function zeros in the thermodynamic limit, where they reach the inverse critical temperature on the real axis. Using less than 100 bosons, we can estimate the condensation temperature for a Bose gas in a harmonic potential in two and three dimensions, and we also find that there is no phase transition in one dimension as one would expect.

show abstract

Lee-Yang theory of Bose-Einstein condensation

et al. 2023

Self Cite

View full text Add to dashboard Cite

Bose-Einstein condensation happens as a gas of bosons is cooled below its transition temperature, and the ground state becomes macroscopically occupied. The phase transition occurs in the thermodynamic limit of many particles. However, recent experimental progress has made it possible to assemble quantum many-body systems from the bottom up, for example, by adding single atoms to an optical lattice one at a time. Here, we show how one can predict the condensation temperature of a Bose gas from the energy fluctuations of a small number of bosons. To this end, we make use of recent advances in Lee-Yang theories of phase transitions, which allow us to determine the zeros and the poles of the partition function in the complex plane of the inverse temperature from the high cumulants of the energy fluctuations. By increasing the number of bosons in the trapping potential, we can predict the convergence point of the partition-function zeros in the thermodynamic limit, where they reach the inverse critical temperature on the real axis. Using fewer than 100 bosons, we can estimate the condensation temperature for a Bose gas in a harmonic potential in two and three dimensions, and we also find that there is no phase transition in one dimension as one would expect.

show abstract

Lee-Yang theory of the two-dimensional quantum Ising model

Cited by 8 publications

References 74 publications

Lee-Yang theory of quantum phase transitions with neural network quantum states

Lee-Yang theory of quantum phase transitions with neural network quantum states

Lee-Yang theory of Bose-Einstein condensation

Lee-Yang theory of Bose-Einstein condensation

Contact Info

Product

Resources

About