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Quantum Computer Shows Zero-Temperature Phase Transition, Challenging Physics Predictions

For the first time, a worldwide team replicated spontaneous symmetry breaking (SSB) at zero temperature, a major advance in condensed matter physics and  quantum computing. A superconducting quantum processor with over 80% fidelity was employed for this landmark work on short-range phase transitions. Brazilian UFSCar, Danish Aarhus University, and Chinese Southern University of Science and Technology researchers published in Nature Communications.

The experiment focused on spontaneous symmetry breaking, crucial to condensed matter physics and the standard model. Symmetry creates conservation laws in physical systems, yet breaking it can create complex structures. The Mermin-Wagner theorem prohibits the development of ordered phases like FM and AFM in short-range interacting systems at any finite temperature in one or two dimensions. One-dimensional systems were widely believed to restrict Spontaneous Symmetry Breaking even at zero temperature.

Symmetry Breaking Spontaneously

In condensed matter physics and the standard model, spontaneous symmetry breakdown is essential. This idea is linked to physical systems and complex structures.

Spontaneous Symmetry Breaking is described in detail from the references:

Central Idea:

Symmetry causes conservation laws in most physical systems. Noether's theorem shows this conservation-symmetry relationship.

However, breaking symmetry can create complicated structures. Spontaneous Symmetry Breaking occurs when a system's ground state or lowest-energy state spontaneously transitions to a state without symmetry in its governing principles.

Traditional Understanding and Challenges (Mermin-Wagner Theorem):

Unplanned Symmetry Breaking in one- and two-dimensional systems is a hot topic for quantum phase transitions at limiting temperatures. In physical systems with long-distance interactions, long-range order like ferromagnetism (FM) or antiferromagnetism (AFM) generally emerges.

According to the Mermin-Wagner theorem, short-range interacting systems in one or two dimensions cannot create correlated antiferromagnetic (AFM) and ferromagnetic (FM) states at any finite temperature. This theorem covers Hubbard and Kondo lattices, Heisenberg chain spin systems, and metal electron interactions.

Spontaneous Symmetry Breaking is assumed to be forbidden for one-dimensional systems even at zero temperature. Compared to its limited temperature equivalent, this field has attracted less attention.

The Experimental Breakthrough in SSB Observation:

The new work simulates Spontaneous Symmetry Breaking at zero temperature for the first time. More than 80% fidelity was achieved using a superconducting quantum processor.

This work focused on replicating dynamics at zero temperature, which is unachievable in reality due to the unattainability principle, the third law of thermodynamics. Quantum computers mimicked absolute zero.

The experiment proved that symmetry breaking can occur in local particle interactions, such as between first neighbours, when the temperature is zero. This violates traditional physics expectations that certain phases are banned for short-range interacting systems at any finite temperature.

SSB in Experiment:

Digital quantum annealing powered the device, which had seven qubits in a superconducting lattice resembling a three-generation Cayley tree (allowing only nearest-neighbor interactions).

The starting state was a classical antiferromagnetic (AFM) 'flip-flop configuration' in which particle spins alternated. Initial state was called “Classical Néel state”.

After that, the system spontaneously transformed into a ferromagnetic (FM) quantum state with quantum correlations and particle spins aligned.

This phase transition from classical AFM to quantum FM-like is clearly attributed. From the ground state of the Néel field Hamiltonian, the AFM phase developed, whereas from the excited state, an ordered quantum FM-like state emerged. Depending on the initial Néel state, FM-like or AFM-like phases produced the system's energy split.

Symmetry in System Dynamics:

The initial Hamiltonian for the Néel state is symmetric in (\hat{M}{z}) (total magnetisation), ([\hat{H}{\text{Néel}}, \hat{M}_{z}]=0)21.

Thus, each adiabatic development from ground or excited Néel states will occur across a separate magnetisation plane. The excited state is positively magnetised, while the ground state is negatively magnetised.

The system also maintained the parity defined by the operator (\hat{\Pi}_z = \prod \hat{\sigma}_z) ([\hat{\Pi}_z, \hat{H}(s)]=0)22. This parity conservation law prevented degraded states with differing parities from mixing during evolution, preventing the annihilation of associated phases22.

Witnessing and Quantifying SSB/Entanglement:

The phase transition and ordered patterns (({C}_{x}^{(i,j)}) were identified and quantified using two-point correlation functions. These functions showed the system's dynamical symmetry breakdown.

The quantum character of FM-like and AFM-like phases was revealed by studying entanglement entropy, particularly the second-order Rényi entropy.

The Rényi entropy was invented by Hungarian mathematician Alfréd Rényi to assess entanglement and its distribution in quantum systems. It monitors subsystem entanglement even in mixed quantum states.The Rényi entropy of a subsystem increases when it is entangled (assuming the system is pure).

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