Quantum models with the Yang-Lee phase transition

summary

The gist

The gist In this article, four different 1+1D quantum models are presented that realize the Yang-Lee (YL) phase transition under a deformation that preserves PT symmetry, and it is shown that in all

In short

Four different 1+1D quantum models—including spin chains, Schwinger model, Blume-Capel model, and a quantum clock model—are studied to realize the Yang-Lee phase transition under PT symmetry preservation. The research shows that in all these models, the critical point is described by a massless bosonic field with an iφ^3 interaction. Numerical results strongly agree with exact two-dimensional CFT predictions for criticality.

Key concepts

Yang-Lee (YL) Phase Transition: This is a type of phase transition occurring in statistical mechanics that happens when a system approaches a critical point along the boundary of its phase diagram. In this context, it is studied under specific deformations that keep the system's symmetry properties intact, allowing physicists to relate it to Conformal Field Theory (CFT).
PT Symmetry Preservation: The study uses a deformation where P: φ ightarrow -φ and T: i ightarrow -i. This specific transformation preserves the combined Parity-Time symmetry (PT), which is crucial because it allows the YL transition to be viewed as a spontaneous breaking of this symmetry, linking it to known critical theories.
Bosonization: This is a mathematical technique used primarily in quantum field theory for 1+1 dimensional systems. It maps interacting fermionic or spin models onto simpler, equivalent bosonic field theories. This method was used specifically for the massive Schwinger model to describe its critical behavior.
Scaling Dimensions: These are numerical values assigned to the lowest operators in a Conformal Field Theory (CFT). They dictate how correlation functions behave as the system size changes. Finding these dimensions and comparing them to theoretical exact values confirms that the models correctly belong to specific universality classes, like the 2D YL CFT.

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This episode discusses

The paper

Quantum models with the Yang-Lee phase transition · Read on arXiv

Erick Arguello Cruz, P Grigory Tarnopolsky

Department of Physics, Carnegie Mellon University

In this article, we present four different 1+1 D quantum models that realize the Yang-Lee (YL) phase transition under a deformation that preserves PT symmetry. These are the antiferromagnetic Ising spin chain in transverse and longitudinal magnetic fields, the massive Schwinger model, the Blume-Capel model, and the three-state quantum clock model. Using the state-operator correspondence, we identify the YL critical point, compute the scaling dimensions of the lowest operators in each model, and find perfect agreement with the exact results for the YL criticality in two dimensions. Using bosonization for the Schwinger model and the Polyakov-Hubbard transformation for the other models, we show that in all of these quantum models the YL critical point is described, as expected, by a massless bosonic field with an i ϕ cubed interaction. In the quantum clock model, this critical field interacts with a massive bosonic field, and we identify the massless and massive states in the Hamiltonian spectrum. In addition, we numerically compute the two-point function of ϕ at the Yang-Lee critical point and show that it grows with distance, in agreement with theoretical expectations.

Transcript

Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Quantum models with the Yang-Lee phase transition".

Mira: The gist In this article, four different 1+1D quantum models are presented that realize the Yang-Lee (YL) phase transition under a deformation that preserves PT symmetry,

Kai: First, who's behind it and why it matters.

Paper summary: Mira: The main thesis is that using the state-operator correspondence, they manage to identify the YL critical point in these systems and then calculate the scaling dimensions of the lowest operators for each model.

Kai: And what's really important is that they find perfect agreement with the exact results for two dimensional YL criticality.

Lev: That connection to exact results is important because it grounds this description in a known, solvable system, even though we are dealing with these deformed quantum models.

Mira: They also demonstrate that in all four of these quantum models, the Yang-Lee critical point is described by a massless bosonic field with an i phi cubed interaction.

Kai: And for the three-state quantum clock model specifically, this critical field interacts with a massive bosonic field, and they manage to identify the massless and massive states in that Hamiltonian spectrum.

Lev: That means they're not just looking at one type of criticality; they're mapping out the whole structure of these different phases in the quantum clock model.

Mira: The paper also notes that for the antiferromagnetic quantum Ising model, their effective central charge ceff is within ten to the power of negative four of the exact value for two dimensional YL CFT <ref:2606.19732#pg2>.

Kai: It seems like they’re checking universality across these different setups, showing that all these distinct models fall into the same YL universality class when you look at this PT symmetric deformation.

Lev: If this holds up, it suggests that the underlying mechanism driving this phase transition is very robust and universal across these different lattice structures.

Kai: So in short, they show a consistent field theory description for these four quantum systems under the PT deformation, and that description has strong theoretical backing.

Conclusion: Mira: The authors took four very different physical setups—from spin chains to massive quantum clock models—and managed to find a unified field description for their critical behavior.

Kai: The main implication is that this massless bosonic i phi cubed theory acts as a universal description for the YL criticality across these diverse one plus one dimensional quantum systems <ref:2606.19732#pg1>.

Lev: For someone building real hardware, it’s interesting because it tells us what kind of field theory we should expect to see when we measure these kinds of phase transitions in our actual experimental setups.

Mira: It suggests that the specific details of the lattice model matter less than the underlying symmetry—the PT symmetry—when determining this critical behavior.

Kai: It means we can use this field theory description as a guide for understanding phase transitions in other complex systems where PT symmetry might be relevant, even if they aren't exactly these quantum models.

Lev: The work confirms that the physical picture aligns with the mathematical structure of the minimal models they are referencing, which is always good for checking our theoretical assumptions.

Mira: In short, this paper solidifies a consistent field theory picture for a broad range of deformed quantum systems exhibiting Yang-Lee criticality.

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