Parent Hamiltonian and intrinsic phase transition in non-Hermitian photonic systems

arXiv:2607.28964 · quant-ph, cond-mat.mes-hall · Submitted 2026-07-31 · Read on arXiv

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

Kai: Today's paper: "Parent Hamiltonian and intrinsic phase transition in non-Hermitian photonic systems".

Mira: The gist The work reports the first experimental generation and characterization of non-Hermitian parent Hamiltonians (NH-PHs) using single photons,

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

Paper summary: Mira: To wrap up this discussion on "Parent Hamiltonian and intrinsic phase transition in non-Hermitian photonic systems," the authors demonstrate that they can experimentally build non-Hermitian systems with specific, tailored properties using this parent Hamiltonian approach.

Kai: The main implication is that we now have a systematic blueprint for designing these non-Hermitian phases by starting with desired ground states encoded in matrix product states <ref:2607.28964#pg1>.

Lev: It means we can use this method to explore non-Hermitian topology and many-body dynamics in photonic systems where the effects are usually very hard to see <ref:2607.28964#pg3>.

Mira: The intrinsic phase transition they found in the N=three model, where you get a level crossing and an abrupt jump in the order parameter, is a specific signature of non-Hermitian criticality that's distinct from what we see in Hermitian systems <ref:2607.28964#pg3>.

Kai: It’s about creating a platform where you can precisely control the non-Hermiticity using parameters like mu, and seeing how that affects the system's behavior in a measurable way <ref:2607.28964#pg3>.

Lev: The method itself relies on this idea of reverse-engineering these phases, which is a powerful tool for understanding complex systems <ref:2607.28964#pg3>.

Conclusion: Kai: So we've seen how they built these non-Hermitian systems from scratch using this parent Hamiltonian idea, and now we're looking at what they actually did with their conclusion on the whole paper.

Mira: They’re essentially saying they managed to design a system where you can dial in exactly the non-Hermiticity you want, and it holds up. The authors are focusing on how this method lets you reverse-engineer these complex non-Hermitian phases.

Kai: It sounds like the main takeaway is that this framework isn't just theoretical stuff for writing down equations; they actually got experimental results that match their design perfectly across different settings.

Mira: Yeah, it’s about proving that you can take a specific target state, build the system around it using this Hamiltonian construction, and then measure if the system actually has the properties they intended. That's a solid claim for a physical realization.

Kai: So what does that mean for someone just listening? It means we're getting closer to designing quantum systems where you control things like chirality directly, instead of just hoping it happens by accident in nature.

Mira: Exactly. They show that this approach works not just for simple states, but they even used it to find a phase transition in a larger system, which suggests this isn't just a trick for small setups.

Kai: It opens up the door to using these photonic platforms for things like advanced sensing or quantum simulations where you need very specific non-Hermitian behavior that's hard to get otherwise.

Mira: Right. The implication is that we have a systematic blueprint now for exploring non-Hermitian topology and dynamics in these kinds of physical systems, which was previously quite difficult to map out systematically.

Beijing Computational Science Research Center · State Key Laboratory of Low Dimensional Quantum Physics and Department of Physics at Tsinghua University · School of Physics at Southeast University · School of Physics and Optoelectronic Engineering at Anhui University · Frontier Science Center for Quantum Information · Hefei National Laboratory

quant-ph, cond-mat.mes-hall

Submitted: 2026-07-31

Updated: 2026-07-31

Comments: 9 pages, 5 figures. Accepted for publication in Physical Review Letters

Journal ref: Phys. Rev. Lett. 137, 110401 (2026)

DOI: 10.1103/7ly2-g3bh

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 88/100

The gist: The gist The work reports the first experimental generation and characterization of non-Hermitian parent Hamiltonians (NH-PHs) using single photons, enabling the construction of systems with

Key concepts

Non-Hermitian Parent Hamiltonian (NH-PH): This is a specific mathematical framework used to construct non-Hermitian quantum systems. It allows researchers to design the system's properties by specifying desired features in its biorthogonal ground states, which are encoded in matrix product states (MPS). This method provides a systematic way to create controllable non-Hermitian systems.
Matrix Product States (MPS): MPS are mathematical objects used to represent quantum many-body systems efficiently. In this work, they were used as the blueprint for constructing the target right and left zero-energy ground states of the NH-PH. By tailoring these MPS, researchers could precisely engineer the non-Hermitian features of the resulting Hamiltonian.
Non-Hermitian Chirality: This refers to a property of non-Hermitian systems where tuning a parameter (the asymmetry parameter µ) causes a change in the sign of an order parameter. In this experiment, changing µ away from 1 directly demonstrated non-Hermitian chirality, showing how the system's behavior flips based on its engineered non-Hermiticity.
Non-Hermitian Phase Transition: This is a critical point in the N=3 model where the system undergoes an abrupt change, signaled by both a level crossing in the energy spectrum and a sudden jump in an order parameter. This behavior is distinct from standard Hermitian phase transitions and indicates a new type of criticality achievable through this photonic platform.

Terminology

Entanglement — 13× in this paper · explained in 3 episodes
Phase Transitions — 9× in this paper · explained in 2 episodes
Non-Hermitian Phase Transition — 7× in this paper · explained in 2 episodes
Quantum Circuits — 5× in this paper · explained in 2 episodes
Antiferromagnetic Correlation — 4× in this paper · explained in 1 episode
Non-Hermitian Skin Effect — 2× in this paper · explained in 2 episodes
Coherence Length — 1× in this paper · explained in 2 episodes
Fidelity — 1× in this paper · explained in 2 episodes
Process tomography — 1× in this paper · explained in 2 episodes
Quantum Physics — 1× in this paper · explained in 10 episodes
Spectral Gap — 1× in this paper · explained in 5 episodes

Summary

The gist The work reports the first experimental generation and characterization of non-Hermitian parent Hamiltonians (NH-PHs) using single photons, enabling the construction of systems with controllable and customizable properties through a direct design methodology.

Construction of NH-PH

The theoretical method of nonHermitian parent Hamiltonian (NH-PH) enables the construction of a non-Hermitian system from a pair of matrix product states (MPSs) with tailored properties<ref:2607.28964#pg2> This construction provides a general framework for systematically exploring intrinsic non-Hermitian phenomena<ref:2607.28964#pg2> The protocol begins by specifying desired non-Hermitian features in the biorthogonal ground states, and encoding them in a pair of predesigned MPSs that serve as the target right and left zero-energy ground states<ref:2607.28964#pg2> To construct the NH-PH, one starts from a pair of shortrange correlated MPSs on an N-site chain under open boundary conditions (OBC)<ref:2607.28964#pg2> Recent theoretical work has shown that given such a pair of MPSs, one can analytically construct an NH-PH for which R⟩ and L⟩ serve as the right and left zero-energy modes, respectively<ref:2607.28964#pg2> The resulting NH-PH for N = 2 reads H = (5)

Experimental Implementation

To experimentally verify that the constructed NH-PH exhibits the intended properties, one implements the imaginary-time evolution to extract both the right and left ground states of the NH-PH and reconstruct them by quantum state tomography<ref:2607.28964#pg2> The protocol involves initializing photons in a maximally mixed state ρ0 = 1/4 using a beam displacer (BD1) together with a set of half-wave plates (HWPs)<ref:2607.28964#pg2> To extract the right (left) ground state of the constructed NH-PH, one applies imaginary-time evolution Uτ = e−Hτ (U†τ = e−H†τ) to the initial state ρ0 with a fixed evolution time τ<ref:2607.28964#pg2> The passive operation U˜τ is implemented via singular value decomposition U˜τ = V DWT, where D is a non-unitary diagonal matrix with the first diagonal element D11 = 1<ref:2607.28964#pg2> This setup provides a general and controllable method to implement imaginary-time evolution generated by an NH-PH in a photonic platform<ref:2607.28964#pg2>

Experimental Results

The experimental results show excellent agreement with theoretical predictions across the entire range of the asymmetry parameter µ, confirming that the engineered Hamiltonian faithfully reproduces the designed biorthogonal ground states<ref:2607.28964#pg2> For N = 2, the order parameters probe non-reciprocal correlations, chiral imbalance, and antiferromagnetic correlations<ref:2607.28964#pg2> The asymmetry parameter µ controls the nonHermiticity of the system: µ = 1 corresponds to the Hermitian limit, while µ ≠ 1 introduces non-Hermitian chirality<ref:2607.28964#pg2> When tuning µ away from 1, ⟨Ochiral⟩ changes sign—positive for µ > 1 and negative for µ < 1—directly demonstrating the non-Hermitian chirality encoded in the MPS design<ref:2607.28964#pg2> Furthermore, the entanglement spectra exhibit a clear dependence on µ: the two dominant Schmidt coefficients split asymmetrically as µ deviates from 1, with the degree of splitting increasing with µ − 1<ref:2607.28964#pg2>

Extension to a new N = 3 model

Having experimentally validated the NH-PH construction in the minimal N = 2 realization, the scheme is extended to an N = 3 model to explore an intrinsic non-Hermitian phase transition<ref:2607.28964#pg2> This transition is manifested by both a level crossing in the energy spectrum and an abrupt jump in the order parameter—a hallmark of nonHermitian criticality distinct from Hermitian phase transitions<ref:2607.28964#pg2> The expectation value exhibits abrupt jumps coinciding with the spectral crossings, confirming the presence of a phase transition<ref:2607.28964#pg2> This behavior points to potential applications in enhanced sensing, where small perturbations near the critical point can be significantly amplified<ref:2607.28964#pg2> The work establishes a systematic blueprint for reverse-engineering non-Hermitian phases, and provides a versatile platform for exploring new properties and phenomena in nonHermitian physics<ref:2607.28964#pg2>

Conclusion

The work reports the first experimental realization of NH-PHs with tailored properties<ref:2607.28964#pg2> The results provide clear experimental evidence that the engineered NH-PH faithfully reproduces both the local and entanglement properties dictated by the designed biorthogonal MPS ground states<ref:2607.28964#pg2> This agreement across multiple order parameters establishes a controlled photonic realization of NH-PHs with designed non-Hermitian properties<ref:2607.28964#pg2> The NH-PH framework can be extended to study non-Hermitian topology, many-body dynamics, and quantum metrology in regimes beyond the reach of existing methods<ref:2607.28964#pg2>

Direct MPS preparation for N = 2

The direct generation of the target AKLT states R⟩ and L⟩ by mapping the MPS tensors onto a quantum circuit is a general approach [79]<ref:2607.28964#pg2> The expectation values ⟨OMPS⟩ agree with the theoretical prediction (solid lines) and matches the values extracted from the imaginary-time evolution in Fig. 2(a)<ref:2607.28964#pg2> This direct measurement of the expectation values of order parameters provides a cross-check of our experiment and confirms that the steady state produced by imaginary-time evolution faithfully represents the target MPSs<ref:2607.28964#pg2> The same strategy can be extended to larger N systems, providing a new approach to quantum simulation of many-body systems<ref:2607.28964#pg2>

Direct MPS preparation for N = 3

The right ground state R˜⟩ is defined by the tensors [A R] (6)<ref:2607.28964#pg2> The left ground state is taken as L˜⟩ = KR˜⟩, where K denotes the complex conjugation operator<ref:2607.28964#pg2> The real part of the ground-state energy becomes negative within two intervals ϕ ∈ (π/6, π/3) and ϕ ∈ (2π/3, 5π/6)<ref:2607.28964#pg2> This signals an intrinsic non-Hermitian phase transition due to the breakdown of the variational principle in non-Hermitian systems<ref:2607.28964#pg2> The expectation value exhibits abrupt jumps coinciding with the spectral crossings, confirming the presence of a phase transition<ref:2607.28964#pg2> This confirms that this phase transition persists upon increasing the system size and is therefore not a finite-size effect<ref:2607.28964#pg2> The conceptual connection between these level crossings and thermodynamic phase transitions in open systems remains an evolving area for future study<ref:2607.28964#pg2>

End Matter

The work provides a practical route for the experimental preparation of MPS states and the direct measurement of expectation values of observables<ref:2607.28964#pg2> The same strategy can be extended to larger N systems, providing a new approach to quantum simulation of many-body systems<ref:2607.28964#pg2> The experimental results show excellent agreement with theoretical predictions across the entire range of the asymmetry parameter µ, confirming that the engineered Hamiltonian faithfully reproduces the designed biorthogonal ground states<ref:2607.28964#pg2> This direct measurement of the expectation values of order parameters provides a cross-check of our experiment and confirms that the steady state produced by imaginary-time evolution faithfully represents the target MPSs<ref:2607.28964#pg2> The same strategy can be extended to larger N systems, providing a new approach to quantum simulation of many-body systems<ref:2607.28964#pg2> The experimental results show excellent agreement with theoretical predictions across the entire range of the asymmetry parameter µ, confirming that the engineered Hamiltonian faithfully reproduces the designed biorthogonal ground states<ref:2607.28964#pg2> This direct measurement of the expectation values of order parameters provides a cross-check of our experiment and confirms that the steady state produced by imaginary-time evolution faithfully represents the target MPSs<ref:2607.

Improvements for AI systems

No-Hermitian Hamiltonian (NH-PH) Construction for System Design: The ability to directly design a non-Hermitian Hamiltonian with prescribed properties allows for the creation of Hamiltonians with tailored properties, such as specific non-reciprocal correlations or chiral imbalance, by prescribing structures in the biorthogonal ground states.
Experimental Verification of Non-Reciprocal Correlations: The system can be used to measure four different order parameters that probe non-reciprocal correlations, chiral imbalance, and conventional antiferromagnetic correlations, providing a direct experimental check on the designed asymmetry parameter µ.
Intrinsic Non-Hermitian Phase Transition Detection: The framework enables the observation of an intrinsic non-Hermitian phase transition, manifested by abrupt jumps of an order parameter when the designated zero-energy modes cease to be the globally lowest-energy states, which signals a nonHermitian criticality distinct from Hermitian phase transitions.
Controllable Quantum Simulation Platform: The approach provides a versatile platform for exploring new properties and phenomena in nonHermitian physics, allowing for the experimental study of ground-state properties and their biorthogonal structure across diverse physical platforms, including photonics, cold atoms, and superconducting circuits.