Many-body thermodynamics on quantum computers via partition function zeros

Partition functions are ubiquitous in physics: They are important in determining the thermodynamic properties of many-body systems and in understanding their phase transitions. As shown by Lee and Yang, analytically continuing the partition function to the complex plane allows us to obtain its zeros and thus the entire function. Moreover, the scaling and nature of these zeros can elucidate phase transitions. Here, we show how to find partition function zeros on noisy intermediate-scale trapped-ion quantum computers in a scalable manner, using the XXZ spin chain model as a prototype, and observe their transition from XY-like behavior to Ising-like behavior as a function of the anisotropy. While quantum computers cannot yet scale to the thermodynamic limit, our work provides a pathway to do so as hardware improves, allowing the future calculation of critical phenomena for systems beyond classical computing limits.

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Use of the Complex Zeros of the Partition Function to Investigate the Critical Behavior of the Generalized Interacting Self-Avoiding Trail Model

Entropy ◽

10.3390/e21020153 ◽

2019 ◽

Vol 21 (2) ◽

pp. 153

Author(s):

Damien Foster ◽

Ralph Kenna ◽

Claire Pinettes

Keyword(s):

Phase Transitions ◽

Partition Function ◽

Critical Behavior ◽

Finite Size ◽

The Self ◽

Partition Function Zeros ◽

Adsorption Transition ◽

Function Zeros ◽

Complex Zeros ◽

Self Avoiding Walk

The complex zeros of the canonical (fixed walk-length) partition function are calculated for both the self-avoiding trails model and the vertex-interacting self-avoiding walk model, both in bulk and in the presence of an attractive surface. The finite-size behavior of the zeros is used to estimate the location of phase transitions: the collapse transition in the bulk and the adsorption transition in the presence of a surface. The bulk and surface cross-over exponents, ϕ and ϕ S , are estimated from the scaling behavior of the leading partition function zeros.

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Partition Function Zeros at First-Order Phase Transitions: Pirogov–Sinai Theory

Journal of Statistical Physics ◽

10.1023/b:joss.0000037243.48527.e3 ◽

2004 ◽

Vol 116 (1-4) ◽

pp. 97-155 ◽

Cited By ~ 14

Author(s):

M. Biskup ◽

C. Borgs ◽

J. T. Chayes ◽

R. Kotecký

Keyword(s):

Phase Transitions ◽

Partition Function ◽

Partition Function Zeros ◽

First Order ◽

Function Zeros ◽

First Order Phase

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Partition function zeros and phase transitions for a square-well polymer chain

Physical Review E ◽

10.1103/physreve.88.012604 ◽

2013 ◽

Vol 88 (1) ◽

Cited By ~ 25

Author(s):

Mark P. Taylor ◽

Pyie Phyo Aung ◽

Wolfgang Paul

Keyword(s):

Phase Transitions ◽

Partition Function ◽

Polymer Chain ◽

Partition Function Zeros ◽

Square Well ◽

Function Zeros

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PARTITION FUNCTION ZEROS OF AN ISING SPIN GLASS

International Journal of Modern Physics C ◽

10.1142/s012918319500068x ◽

1996 ◽

Vol 06 (06) ◽

pp. 819-843 ◽

Cited By ~ 8

Author(s):

P. H. DAMGAARD ◽

J. LACKI

Keyword(s):

Partition Function ◽

Spin Glass ◽

Spin Glasses ◽

Lattice Models ◽

Partition Functions ◽

Distribution Of Zeros ◽

Partition Function Zeros ◽

Polynomial Mappings ◽

Ising Spin ◽

Function Zeros

We study the pattern of zeros emerging from exact partition function evaluations of Ising spin glasses on conventional finite lattices of varying sizes. A large number of random bond configurations are probed in the framework of quenched averages. This study is motivated by the relationship between hierarchical lattice models whose partition function zeros fall on Julia sets and chaotic renormalization group flows in such models with frustration, and by the possible connection of the latter with spin glass behavior. In any finite volume, the simultaneous distribution of the zeros of all partition functions can be viewed as part of the more general problem of finding the location of all the zeros of a certain class of random polynomials with positive integer coefficients. Some aspects of this problem have been studied in various areas of mathematics, and we show in particular how polynomial mappings which are used in graph theory to classify graphs, may help in characterizing the distribution of zeros. We finally discuss the possible limiting set of these zeros as the volume is sent to infinity.

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Partition Function Zeros at First-Order Phase Transitions: A General Analysis

Communications in Mathematical Physics ◽

10.1007/s00220-004-1169-5 ◽

2004 ◽

Vol 251 (1) ◽

pp. 79-131 ◽

Cited By ~ 15

Author(s):

M. Biskup ◽

C. Borgs ◽

J.T. Chayes ◽

L.J. Kleinwaks ◽

R. Koteck�

Keyword(s):

Phase Transitions ◽

Partition Function ◽

General Analysis ◽

Partition Function Zeros ◽

First Order ◽

Function Zeros ◽

First Order Phase

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Partition function zeros for the two-dimensional Ising model

Physica A Statistical Mechanics and its Applications ◽

10.1016/0378-4371(84)90028-1 ◽

1984 ◽

Vol 129 (1) ◽

pp. 201-210 ◽

Cited By ~ 34

Author(s):

John Stephenson ◽

Rodney Couzens

Keyword(s):

Ising Model ◽

Partition Function ◽

Two Dimensional ◽

Partition Function Zeros ◽

Function Zeros

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Probing phase transitions of holographic entanglement entropy with fixed area states

Journal of High Energy Physics ◽

10.1007/jhep12(2020)084 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Donald Marolf ◽

Shannon Wang ◽

Zhencheng Wang

Keyword(s):

Phase Transitions ◽

Entanglement Entropy ◽

Many Body ◽

Btz Black Hole ◽

Holographic Entanglement Entropy ◽

Volume Limit ◽

Cutoff Dependence ◽

Diagonal Approximation ◽

Fixed Area ◽

Many Body Systems

Abstract Recent results suggest that new corrections to holographic entanglement entropy should arise near phase transitions of the associated Ryu-Takayanagi (RT) surface. We study such corrections by decomposing the bulk state into fixed-area states and conjecturing that a certain ‘diagonal approximation’ will hold. In terms of the bulk Newton constant G, this yields a correction of order O(G−1/2) near such transitions, which is in particular larger than generic corrections from the entanglement of bulk quantum fields. However, the correction becomes exponentially suppressed away from the transition. The net effect is to make the entanglement a smooth function of all parameters, turning the RT ‘phase transition’ into a crossover already at this level of analysis.We illustrate this effect with explicit calculations (again assuming our diagonal approximation) for boundary regions given by a pair of disconnected intervals on the boundary of the AdS3 vacuum and for a single interval on the boundary of the BTZ black hole. In a natural large-volume limit where our diagonal approximation clearly holds, this second example verifies that our results agree with general predictions made by Murthy and Srednicki in the context of chaotic many-body systems. As a further check on our conjectured diagonal approximation, we show that it also reproduces the O(G−1/2) correction found Penington et al. for an analogous quantum RT transition. Our explicit computations also illustrate the cutoff-dependence of fluctuations in RT-areas.

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