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This article comes from Weixin Official Accounts: Fanpu (ID: fanpu2019), by Carlo

A sport and a pastime: Model design and computation in quantum many-body systems, Chinese Physics. B 31 127101 (2022). It has only been two months since the article was published, but the world has changed as fast as a dream in these two months. Moving through a divided world, we can hardly tell whether reality is just a substitute for dreams, or whether too many people in the world have lost their memories and become simply drifting with the wind. Before we lose our memories, here are some notes on the physics of model design and computational solutions for quantum multibody problems in the review article, and our thoughts on completing this 30-plus page scientific paper. Hope to be able to leave some credit records in this world without credit.

A Sport and a Pastime is the masterpiece of James Salter (1925-2015), a famous American novelist. This novel not only brings the American minimalism style inherited from Hemingway to the extreme, but also reveals to readers the height that imagination, the main tool of artistic creation, can reach.

Set in France in the early sixties,"I" meets Dean, a wandering Yale dropout, in Paris. "Me" and Dean drive around Paris and the provinces in an antique sports car, having fun until Dean meets Ann-Marie, a country girl, a pure and fiery dream that unfolds a sensual love story that ends tragically. "I" follows Dean and Ann-Marie's fiery encounter in the quiet French countryside, leading the reader personally into the dizzying and thrilling depths of seductive emotion. The tragic ending of the story makes one ask: what is love, beyond the short time and all the illusory appearances attached to it? Is emotion created in art only so that we can experience life together and apart in this way? This tragic novel about love is actually Salter's own ambitious and tortuous attempt to explore the meaning of storytelling itself, and it clearly reveals to the reader the deep reasons why people, often unconsciously or naturally, are driven by imagination to engage in tireless creative activities.

Creative activity in science, as in art, has deep causes, driven by imagination, often unconsciously or by nature. And this 30-page review article before the reader （A sport and a pastime: Model design and computation in quantum many-body systems) is what we want to express, and it is precisely in the creative activities of designing and computing quantum many-body physical models that we have been full of imagination for several years--in the days and nights of hot burning discussions and calculations, on the fronts where quantum many-body air masses meet. In the vast open space of physical reality and theoretical models-the process of a desperate seagull struggling to spread its wings upward, roaming among cumulonimbus clouds, being embraced by the stars rising above the horizon, and then entering personally into the dazzling and thrilling depths of knowledge.

The author reminds: The next three paragraphs will introduce the physics of quantum multibody computing in the review article. Readers who are not interested can skip it directly without affecting their reading.

The first part of the review introduces the frontier results in Determinant Monte Carlo method and quantum critical metal model. The Hamiltonian of this kind of model contains the free fermion part, the spin (boson) part with quantum critical dynamics, and three terms of interaction between the two. Such a model design allows us to use the critical dynamics of bosons to drive fermions to produce various novel quantum correlation phases such as superconductivity and non-Fermi liquids (see also the author's previous text,"White horse is not horse, non-Fermi liquid-non-Fermi liquid","How much love can there be in one's life"). Our calculations show that critical fluctuations lead to pairing, superconductivity and pseudogap behaviors. From the self-energy analysis, we reveal that the quantum self-energy can be obtained by subtracting the contribution of thermal fluctuations from the Monte Carlo calculation at finite temperature, which is consistent with the theoretical frequency power law. We summarize the critical scaling behavior of bosons in such systems.

In the second part, inspired by the non-Fermi liquid exact solution of SYK model, we design Yukawa-SYK model without sign problem and perform quantum Monte Carlo simulation on it. By coupling fermions and bosons together with random intensities, the coupled system always exhibits gapless quantum critical behavior no matter how far the bosons deviate from the critical point. Therefore, a new quantum critical point, self-tune quantum criticality, has been discovered, which allows us to focus more on the non-Fermi liquid phenomena emerging in the Yukawa-SYK model without worrying about parameter adjustments, and the accompanying superconducting pairing and critical scaling behavior.

In the third part, we show how to design models and calculate numerical results in flat-band corner quantum molar systems, such as corner bilayers, transition metal chalcogenides, etc. Firstly, quantum Monte Carlo and tensor network renormalization group calculations are carried out for the real-space model (see also the author's previous text, Samadhi of Corner Graphene). Then, we develop a momentum space quantum Monte Carlo method that strictly obeys the long-range Coulomb interaction. After projecting the Coulomb interaction onto the flat band, we prove that the flat band system has superior quantum geometry properties, which can ensure that the calculation is not affected by the fermion sign problem even if the kinetic term is added at the electric neutral point. Further, we discover the symbolic boundary theory in correlated flat-band systems (see my collaborators detective novel, The Aron Detective Monte Carlo Symbolic Problem) and extend momentum Monte Carlo calculations to a wider range of parameter spaces (other integer fillings, attractive interactions, etc.). We calculate the symmetry breaking mechanism and the low energy single particle and collective excitation modes of the system under different integer fillings. For the corner transition metal chalcogenide compounds, we give the temperature and doping phase diagrams of the superconducting and Bose fluids in the system by modifying the interaction form.

……

In fact, the results included in the review and the effort put into obtaining them are far beyond the thin and slightly rigid sentences above. At the time of publication, I always feel that these achievements are more like barbed cones, clusters, such as the distance between imagination and physical reality, that is, personal, but also some far away, some of the contents are too complex and heavy. In the night, in dreams, they seem to rise up one by one, in shadows of theoretical bones and numerical flesh, and wander through the phase diagrams, visiting us like human cannons, asking us constantly about the limits of existing knowledge, the limits of current calculation, and the eternal truth about imagination and creativity.

When it comes to truth, it's easier said than done. Years, decades, decades of hard work are but scars in the flow of time. Truth is fluid, and the dream questions continue at this moment. Have you explained the experiment? Do you understand the essence of where topology and interaction intersect? Can you climb over the walls of exponents to the depths of the mysteries of long-range quantum entanglement behavior? Are you an expert? Do you have funds? Do you have a quote? You want a hat? Do you still have a spot? Do you want to go home? Have you ever been infected? Can you leave? Could you write me a letter of recommendation? Do you want to seek refuge from the boss? Are you a writer among scientists, or are you a writer in physics? What are you implying? Is what you're trying to say, evasive or not? Are you a helpless witness to history or an abrupt interloper? Most of these questions we have no answers to, and the answers we reluctantly give are clearly inadequate. All we know and can do is to insist, almost religiously, that the hour is approaching, that experimental phenomena and theoretical developments are at hand, that the flute is sounding, that man will leave the shore, that the ship of calculation will sail in the monsoon, that Christ will walk on the water as in legend, and that truth will come as promised in faith.

Daily research work is not as romantic as a game and a pastime. Daily research work is full of unpredictable cramps and embarrassment. Practitioners often need to bear double paradoxes: suffering through real time in imagination and pursuing imaginary scenery in reality. We must accept, then, that for a longer time to come, in a collection of physical calculations, theories, and experiments, our voyage will have no beginning or end, but only the most earnest conviction that guides us all the way out to sea, against the whimpers of the waves, occasionally stopping before the magnificent landscapes of human spirit and mysterious nature, with a reverent hope that when we finally cross the empty sea, perhaps our ships will be loaded with colorful shells.

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